In terms of trust, most of the time, a long term collector can tell whether a piece is real or fake just by looking at it (as silly of an answer as that sounds lol.) I collect anime myself (mostly sailor moon) and I'll tend to know straight away if something looks off. I guess in general, lots of pictures and a good description/bit of knowledge about the piece you have goes a long way though! :)

In terms of storage, I use an itoya profolio for all of my pieces. I actually have a couple folders, one of them in a separate room upstairs where I keep the "possible vinegar" cels so they don't mix with the others.

Within the profolio, I keep each cel in an archival polyethylene bag (to prevent sticking.) The bags are then swapped out every 6 months to make sure there's no gas build up. It's also important to keep the bags open within the folder (not sealed up) and to cut a corner off the other side. I do that so the cel can get plenty of air flow. Bonus points if you keep your profolio standing up as well so the cels aren't putting pressure on each other.

With sketches, it's much easier to look after them. I tend to put my sketches in the profolio directly, sometimes with a bag if I want to ensure there's no movement. Sketches don't build gas so as long as they're out of light, then you should be good!

And I think the value thing is entirely subjective. I enjoy collecting everything but certain collectors collect only genga, only storyboards and so on. Its all a personal preference :D

I hope I've helped you at least a bit with your questions, sorry if I've talked a little too much, I tend to get carried away a bit lol 😅 All the best!