Okay, I get that the kids were deliberately trying to avoid running into their "natural" past selves in their time jumps. That being said, when they kept going back so the one could keep retaking his chemistry exam, how were they not running into their counterparts from their past jumps, who were also trying to give him a chance to pass his exam? Not to mention David somehow taking the place of his past traveler self for the talk with Jessie at Lollapalooza without any trouble.
I think they were essentially erasing their future selves. If they went back before they went back the last time, they wouldn't be there to go back and meet their other time traveling selves. Though, I don't know how that would work with when David replaced himself at the music festival. That's probably a plot hole that we're supposed to ignore.
So, they create a rule about no social media, and they have no problem when Quinn gives them their travel itinerary because he posted everything on social media.
He wasn't posting it on social media - he was reading reviews of the event that he had downloaded before they traveled back, to work out what were the best parts of the event to be at.
When David destroys the original heart of the time machine and all the blueprints that his dad had back in 2004, he got erased from existence; that makes perfect sense, as there's no way he could go back if they'd never had all that to start building the time machine from. But then, why was the camera still there?
It seems laws of time travel aren't the same for living people and inanimate objects. When Jesse is erased from existence, her keys remains on the ground. So it seems that living people can erase themselves, but once an item is sent to the past, the laws of causality don't apply to them anymore.
Which really makes zero sense. If Jessie was wiped from existence, David would have never had the keys to begin with. This scene was shot before their first experiment, and before Jessie and David "got together." This also begs the question of why the police were after David at the end, as Jessie would have "disappeared" before she joined the group. Really, for a time travel movie that wants very badly to demonstrate the butterfly effect, it seems to ignore it's own logic.
Personally I'm questioning why, if he was trying to destroy it all, he neglected the camera with everything else.
Probably, he wanted it to remain as a record of what they did, for his new timeline counterpart. That was the whole point of getting everything recorded in the first place.
Did David destroy the glass box? If he did, what exactly is the glass box made of that it can perform fusion but can be safely burned in open air? And if he didn't, doesn't that defeat the whole point of his trip?
The box was definitely destroyed, considering he was erased from existence afterwards. Presumably, the glass box had components extremely sensitive to temperature and the fire permanently damaged it beyond repair.
The machine runs on hydrogen, or at least requires it to work, so they steal some the first time. After they get up and running, though, they could just buy as much as they need, and anonymously replace what was stolen, because they won the freaking lottery. The whole end bit with breaking into the school (again) should have been totally unnecessary.
Cost wasn't the issue. The fact was that in order to buy hydrogen, he needed a special permit according to the movie.
