Who and where was Charlottes mate? (Yes, she must have had one since she had babies at the end.) He makes absolutely no appearance throughout the entire story.
You do realize that many species of spiders tend to eat the mate? If she didn't eat him then, he probably died after mating.
Even so, when did the mating take place? Charlotte was first introduced several months before she laid her eggs.
Well, there's two explanations for this. Some species of arthropods (insects and spiders) develop their eggs a good while before they lay (how long this would be varies) or she met and mated offscreen.
Why didnt Fern try to talk her uncle out of killing Wilbur?
This was more or less noted on the Fridge, where someone brought up that the idea of him slaughtering Wilbur might have been seen as a learning experience (that animals are to be "cared for, not coddled", in simple terms), so her talking him out of slaughtering him might not have done any good.
It still seems rather harsh if you ask me, for quite a few reasons. One, Wilbur was Ferns pig first and she had spent a lot of time loving and caring for him as if he were her own child. Plus, Fern was able to talk her father out of killing him in the beginning which is why Wilbur was her pig to begin with. Also, she is the one who sold him, and in the beginning it obviously never occurred to her that he might be slaughtered. And she is Zuckermans niece. If my niece sold me a pig and I knew she wouldnt want him to be slaughtered, I would reconsider that. Point aside, it also bugs me that Zuckerman would slaughter a pig that had a name. Thats almost like slaughtering your pet.
Yes, I suppose it is, however, as noted, Fern is a farm girl and, if she's to continue in the farming business, then, well, her family might have felt the trope being a case of The Only Way They Will Learn, in which case, she'd have to learn to learn the hard way. If anything, this might be why he was sold was so she could learn. He wasn't sold by her, but her father, and part of the reason as to why he agreed to spare Wilbur is so she would learn how hard it was to raise a weak, runty pig. Likewise, you could see it as a case of Values Dissonance, as the story was written/published and probably takes place in the 50s, where some of the stuff the guardians do might be considered questionable nowadays but normal back then.
In the live-action version, we do see Fern sitting on an overturned bucket drawing outside the barn while Zuckerman and Lurvy engage in a discussion regarding the need to prepare the smokehouse for Wilber just several feet away. After this catches her attention, we see her frantically get up and run in their direction. In the next scene, she's complaining to her parents about what she'd overheard to which her father responds that Wilber legally belongs to Zuckerman and as such he's within his rights to slaughter him. Fern's father would not have brought this subject up while convincing her to sell to Zuckerman because it would have just served to turn her off the idea. I believe this is more attributed to the time period and that this is a farm family than a lack of consideration for a child's feelings/attachment to an animal. It's important to note that this appeared to be set in the '50s and from what I've seen that was a time when parenting was founded more on instilling experience than communication particularly so for a farm family. E.B White established this in the Zuckerman family with Fern's father allowing her to nurture Wilber in the first place and remember on a farm animals are intended to be raised and kept as providers whether it be of material, food or transportation, not as pets.
Live Action Examples
At one point in the film, after Charlotte shows off the work in her web, one of the cows while commenting on her work and how it will affect Wilbur says that she's "glad nobody eats cows." But people DO eat cows. Okay, I get these are probably dairy cows, but the statement is still incorrect. (In fact, I think I've eaten more cows than pigs myself.)
And how would a dairy cow know that?
It could be that the cow was referring to dairy cows themselves and not steers (which, if I'm correct, tend to usually get slaughtered for meat).
The most likely explanation is that it's supposed to be a joke about how cows are morons.