If 食べれる means "can eat", 食べれます means the same but polite, and 食べれません means "can not eat" but in its polite form, how do I say "can not eat" in the nonpolite form?
Another little question: how can I say "can be". For example, "I can be that person".
First of all, it should be 食べられる rather than 食べれる, although the latter form is used. See this link.
Once you have conjugated a verb into the potential form it behaves just like any other iru-eru/group 1 (whatever you want to call it) verb.
As you probably already know, to make a group 1 verb negative you just remove る and replace it with ない. So we get 食べられない.
Furthermore, ない just behaves like an i-adjective so you can get the past tense exactly as you would expect: 食べられなかった. Conjugation in Japanese is really logical :-)
I'm not a native speaker, but I can't think of any way to turn 'to be' into potential form. My guess is that this isn't a natural thing to do. If had to say "I can be that person" I think would use なる (become) and say: あの人になれます。
The verb for “to be”, when applied to people, is
いる. Potential form of it is
いられる, so in theory you could say something like
[私は]あの人でいられる, though it would be a really awkward phrase and I doubt it would get your meaning across. It’s better to use
なれる(can become), as mentioned by others. I think the only common usage of
いられる I’ve seen is for wishes, e.g.
[I wish that you] stay(=can be) in good health this year as well
[I hope that you] stay cheerful