There's not really a point; all they want is to be played with, which isn't benefitted by a reveal. The toys are also aware that if they were to demonstrate their sentience, this could turn into a huge worldwide crisis, with toys everywhere in danger of being experimented on, imprisoned or destroyed.
Why is the masquerade in the first place, then? The whole thing would just be seen as a normal facet of life.
There's a reason possessed toys are a staple of the horror genre. If Woody were to so much as twitch in front of Andy, or change his expression (say his mouth opens just enough to show a toothy grin), Andy screams in blood-curdling horror and never plays with Woody ever again. Woody doesn't want to risk scaring Andy or any other child if he can. He only did that to Sid because he was asking for it.
Why does Buzz follow the crowd if he isn't aware of the fact that he is a toy?
Because he mostly goes along with what the other toys do. He thinks they're an alien culture on an alien planet and is wisely following the adage "when in Rome, do as the Romans do". According to one of the unpurchased Buzz Lightyear dolls in the second movie, Star Command has ordered all space rangers to wait in "hyper-sleep" (read: the Buzz Lightyear dolls sitting in their boxes without revealing their sentience). With that in mind, it's also possible Buzz is continuing to obet this rule from Star Command.
If toys can be alive, what about stuff like toy telephones? What differentiates them from a "grown-up" telephone?
Since a Little Bo Peep lamp figure can also be alive, don't see why not.
What constitutes a "toy"? In Toy Story 2, Hamm states that "the lawn gnome from next door" is alive, so what other things can come alive? What if someone makes their own toy, will that come alive too?
Anything the kid considers a toy comes alive. We see this happen in the fourth movie, with Forky. Not sure what the limits of it are, even some normal toys aren't alive, but it does seem to work that way.
There's some Nightmare Fuel in this, given Forky is clearly tortured by his existential crisis of being half-garbage, half-toy. Every time a child churns out some half-hearted craft a paper doll, a plasticine animal, a sock puppet, etc. does it live some brief, painful life before being thrown in the trash?
Why does Andy only write his name on some of his toys?
Buzz thinks that Andy writing his name on him meant his accepting him into their culture, which implies all of them got Andy's name written on them. The other toys were, however, impressed that Buzz got permanent ink; the others might have rubbed off. Either that, or he only puts his name on toys that he's likely to take out of the house. You wouldn't take your piggy bank to school to play with, it's not going to get lost, so why bother?
Why does the Woody doll have teeth if his "toy mode" doesn't have an open-mouth smile?
Is Play-Doh considered a toy, even though it doesn't have a "true" form? Furthermore, if it is, and it comes to life like any other toy, what happens if it dries out? What about the kids who eat their Play-Doh?
In the outtakes for Toy Story 2, Mrs. Potato packed Play-Doh into Mr. Potato Head's compartment. It didn't seem to be alive.
How come in the movies, their eyes can come out individually when the ones in Real Life have their eyes were attached together as one piece?
Potato Head had sperate eyes in 1952 until around the 1980s, perhaps so kids wouldn't have missing Mr. Potato Head eyepieces or because of choking hazards.
Related to the above: How does Andy's Potato Head have arms that come off so easily when the Real Life ones don't?
When Mr. Potato Head was redesigned in the 80s, for a brief period of time, he did have bendable arms that were permanently attached to his potato body; it wasn't until the 90s or so that his arms became detachable. Though it does raise the question how Andy has this odd Potato Head that has both features of old and new ones.
Woody's got a holster, which seems to imply he has a gun, but the collectors seem to think he's complete without one, implying he never had one in the first place.
He may have originally had one, but lost it. For something that small it might be a common occurence to the point that collectors thank their lucky stars they can even find a Woody doll in the first place.
Accessories for toys only really started being common when the increased use of plastics made toys overall cheaper to produce and manufacture on a large scale; Woody was before that age, so the makers might've deemed it too costly.
Isn't the cowboy hat that Andy wears throughout childhood Jessie's hat?
A WMG is that Emily (Jessie's first owner) is Andy's mother. Emily had the hat, it is not shown in the box of donations Jessie was in, and she was shown to be growing up in the 70s/80s.
Why are the toys against moving in front of humans (sans Sid), while moving in front an animal (e.g., Scud, Buster) is perfectly acceptable? Double standard here...
If humans knew toys were alive, they would probably try to experiment on them in some way, which probably would destroy the purpose of toys: as playthings for human children. Animals, on the other hand, don't really care; Scud and Buster are both perfectly happy playing with Woody and Buzz.
How does Buzz retract his wings? Andy can likely retract them by pressing down on them, but how does Buzz do it?
A shot in the 1 where Buzz "flies" to Andy's car and drops in through the sun roof shows they can retract on their own. Presumably, the same way toys can open and close their mouths or move their limbs without having physical mechanisms (or even joints) to do so.
Does Mr. Potato Head hate Woody or something similar? He always talks to him rudely, he was the only one who made jokes about him when Buzz came to Andy's bedroom, and he led the anti-Woody ambush in first movie.
Potato Head's pretty much shown as a bitter, pessimistic jerk who automatically thinks the worst of everyone, for the most part. He doesn't hate Woody per se, but it's implied he himself is jealous of Woody being the leader and not him, not to mention he seems to think Slinky is being a major kiss-up to Woody.
Do toys feel pain when they're not "alive"?
It's very likely they do, but their involuntary "stay still" instinct overrides any reactions to said pain. Woody very likely felt the pain of getting his forehead burned by sunlight focused through a magnifying glass, but couldn't show any reaction to it until Sid left the room.
Word of God states that toys, even ones who think they're "real" like Buzz, have an involuntary instinct to freeze up as toys when they're around humans. But it's also true that they can move and talk with humans if they so desired, namely when Woody is trying not to get his head blown up in 1. At one point does this survival desire override instinct?
Chances are, if Woody belonged to Sid and wasn't trying to get back to Andy he wouldn't say or do anything.
Why does Buzz have a laser? Seems like it's asking for a lawsuit.
Most likely there's a warning of some kind on the box Buzz came in. As for lawsuits, quick Google says that most laser pointers don't exceed 5mW and don't transmit enough energy to damage anything before your blink reflex kicks in.
Where do Toys' sentience came from? For that matter, when do toys become alive/sentient?
4 seems to indicate the sentience comes from belief whether something is a toy or not.
Buzz's wings pop out with enough force to tear through duct tape (it was how he got off the rocket in time). Isn't that kinda unsafe for little children to play with? Plus, why didn't he do that earlier?
Buzz's wings were faster and more powerful than they would be normally, because Buzz was in control and not Andy. It's like how Woody can move all of his fingers when he's talking to the other toys, but to Andy, all he'll ever have is a thumb and four closed-up fingers. To Andy, Buzz's wings will only ever be a light pop and fwoosh, while when Buzz needs them to tear duct tape, they will. Besides, maybe the duct tape was old and dilapidated. When Sid attached the rocket to Buzz he was all depressed about being a "stupid, insignificant toy" and therefore had accepted his fate of being blown up. By the time Woody had convinced him otherwise, Sid had woken up and taken him outside for the "launch" and couldn't escape without being noticed.
Can battery powered toys move on their own?
Depends on what exactly the batteries are powering. For example, Buzz's batteries mostly power his electronics, like his lights and his sound chip. For a toy like RC, batteries are much more vital, because they power his source of locomotion. If RC has no batteries, he'd still be "alive," but he would be incapable of moving under his own power, since his "engine" wouldn't have power, like a car with no gasoline.
How come humans apaprently are loud enough toys always get advance warning they're coming?
Humans (even the children) are huge giants compared to the toys. Even if a human is walking and talking normally, it probably sounds extremely loud in the toys' ears. You would probably hear Godzilla's steps even if he was just going about his business.
Why do the toys never employ the strategy of "breaking the rules" and revealing their sentience to humans in the sequels?
Sid is just a child, so no one would believe him, and there's not much he'd can do about it. Most times the toys are alive around humans, there's a lot of them around, so keeping up the charade would be worth it. There are other parts in the series where they take risks (such as in 2 where they cross a street, or in 3 where Woody writes to Andy to bring Bonnie), just none where they reveal themselves to people because there's a way around it. In other words, they have done things that at least severely risk revealing themselves.
Mr. Potato Head's eyebrows lack consistency. They are not shown to have any peg or hole to attach to, nor does there seem to be any piece to attach them to his eyes (like his nose and 'stache), yet they always separate from his eyes whenever he falls apart.
Who makes the rules that toys have to stay still? Is there an organization? A deity? There's no punishment for breaking them...
The toys becoming inanimate when humans are looking is an involuntary instinct. Obviously, a lot of social conditioning has been laid on top of it, like the way they always make sure to return to their prior position when someone walks in the room. And also, it seems like toys CAN resist this instinct, as seen at the end of the first film. But unless they make the effort, they'll go still automatically when a human shows up.
Why does Andy have a Bo Peep figure? All his other toys are traditional boy's toys or at most gender-neutral.
Bo isn't one of Andy's toys. She and her sheep are part of a lamp that belongs to Molly; Andy just uses her as a love interest for Woody to have to save.
What do toys do if they or a part of them is swallowed?
If an entire sentient toy is swallowed they could probably attempt to trigger the human's gag reflex from the inside. If a part of a toy is swallowed, it'd probably depend on who swallowed it; as noted above the toys only freeze around humans, so if a dog swallowed Potato Head's ear Potato Head could probably try to get the dog to choke it back out; if it's a child the toy might just bend the rules and call for an adult's help.