There's no way Yukiatsu's dress actually belonged to little five year-old Menma, unless he has separate ones for smelling and crossdressing.
I believe he just found one in a bigger size. I mean it's not like it was the only dress like that in the world. On a seperate note...
Where does it state their ages? I thought they were about 9 or 10 when they were kids, and that now the gang is around 16 or 17.
I always thought the incident with Menma (her death) happened when they were 6, so now they would be 16.
No. Anaru specifically mentions right in the second episode that the Nokemon game that Jintan was buying came out five years ago. And he got that game because it was the version that they played with Menma. At most, the incident when she died happened five years ago.
How exactly did Menma die? I get that she drowned but how? Did she fall into the river by accident while chasing Jinta? Did she fall off a ledge while balancing on it? What the hell happened?
It's all but stated that she somehow slipped on the path while she was running and fell down the hill, probably hitting her head and being knocked out before drowning, similar to what happens to Leslie in Bridge to Terabithia.
If Menma died when they were kids, approximately 7-10 years ago, where was her spirit in the interim? Was she just hanging out in the aether or something?
She died 5 years ago, as mentioned above, She most likely was watching over them but wasn't able to just appear, even in front of Jintan.
Menma was able to affect things in her family's home. Why wouldn't she have made sure to leave them some kind of note? Or something? At least attempt to help her mother come to terms?
She seems to have retained the mentality of a little girl, and since she was as much ten when she died...
She also says that she was unable to write in the notebooks in her house, suggesting that she did try to make some form of contact but was unable to.
It may be specifically because of Menma's mother's ultra intense grief. It could've unadvertedly created a block on Menma's capacity to directly leave messages to her and others, since she's too hurt and depressed upon even thinking of the death of her daughter. It's not helped by Memna noticing it, seeing her mother suffer, and ultimately refusing to do it again.
Just why is Menma older now? Ghosts can age?
She could've used her ghostly energy to make herself look the way she would look if she was still alive. In other works involving ghosts (like Haunted Junction), it's stated that the spirits of dead people are sometimes able to do so if they wish... but often at the expense of draining themselves of energy and eventually dissolving away (Neither going to Hell or Heaven). How does this not apply to Menma, we don't know. Then again, she didn't start appearing in Jintan's space right after her death.
The hypothetical Afterlife is sometimes depicted with a standard age set for all the people there. Instead of the typical case of having people remain the age they died at which would seem to penalize you one way or another. This may have been the author's choice of what that age would be, or at least relative stature.
If proving that Menma was really there was so simple as writing in her notebook in episode 8. Then why the hell didn't Jintan made Menma do that in front of the gang earlier? I can buy that Menma being mentally 10 years old would make her not realize this sooner, but what is Jintan's excuse? he's not exactly a moron is he?
Jintan has a subconscious desire to keep Menma to herself here amongst the living that he struggles with, and thus monologues that he doesn't really need to think about it; Yukiatsu later discusses this possibility with the rest of the gang after Menma's ghost is proven to be real. Menma simply desires to stay with her friends and also monologues that she doesn't really need to think about it, but she comes to acknowledge that she needs to pass on and fulfill her wish for everyone else to move on. Both were Obfuscating Stupidity as to find an excuse not to change the status quo and move on.
At one point, Menma takes a bath and comes back to Jintan's room wearing nothing but a towel. This one scene raises so many questions...
Where was Menma's dress in all this?
Wherever a dress goes when you take a shower. I never wore a dress, so I wouldn't know. Maybe getting washed or maybe on Jintan's bed.
Since it's probably a regular towel, wouldn't other people be able to see it? That could have been a way to prove to the others that, maybe not Menma specifically, but something was there and couldn't be seen.
Every time that people (anyone) experiences the effects of Menma interacting with things, it's claimed as the wind. Door opened/closed? Wind. Good-sized portable light-post moved? Wind. Fliers fall to the ground? Wind. Diary of a dead girl falls to the ground? Wind...But there's no wind in the clubhouse! I mean, Jintan's father probably thinks his bed has a pile of clothes in it which is why he sleeps on a couch.
In the first place, why does Menma need to take a bath when she's a ghost? And if it's because she can get dirty, doesn't it kind of defeat the purpose that she changes back into the exact same dress afterwards anyway?
Menma can get dirty, and it shows us this.
Why is Jintan's father so ridiculously mellow about his son's behaviour? Jintan is a hermit and a truant, and only spends his time eating, sleeping and playing video games. It's established that Jintan is less than 18 (as he wasn't able to buy fireworks), so he is still his father's responsibility. What about Jintan's future? And also since Jintan's father can't see Menma, Jintan would seem to be talking to himself. If Jintan's father loves his son (which we have every reason to believe), why does he intervene and send him back to school? Or to a doctor at the very least? On a similar note, why did absolutely nobody find it unusual that Jintan was absent for an entire semester?! You'd think the police or the school would get involved at some point.
Jintan is obviously still heavily grieving over the deaths of TWO of his loved ones. His father doesn't want to force him into anything that will make him even more depressed. Also, high school isn't compulsory in Japan. It's not that unusual for people to never attend, like Popo.