Technically, yes. Well, sort of. "Mình" is reflexive and thus has technically no restriction on being used like that since "we" would include the speaker and thus making the reflexive "mình" technically not in error, but it's just weird. In practice, absolutely no one will understand it that way. That's imprecise language at it's best (worst?). If you want to say "... our bread," you'd say "tôi ăn bánh mì của chúng tôi" (or "... của chúng mình").
Nope. It can be viewed as such but if you want to be more specific you can just chuck in "đang" before the verb. "Tôi đang ăn bánh mì của mình". Another thing to note is that mình can often mean your own, not necessarily another person's own. So in colloquial speech especially in South Vietnam: "bạn ăn bánh mì của mình" can be interpreted as meaning "you eat/are eating my bread".
It could be plural in the same sense that "you" could be plural, so you could say it to mean "our," but Vietnamese doesn't really have plural words in the same sense as English. For instance, a woman might call out "mình ơi" and would be understood that she's probably calling for her husband - definitely not a plural use in that case. But you could use it in the sense of "của mình" where it simply means belonging to me/you/us depending on context.
"Mình" literally means body, but I've also never heard it used in that way, either. Of course, thanks to Duolingo, I've also used the word "mình" more in the past few weeks than since I've started speaking, so there's also that.
I don't live in Vietnam anymore, so my usage is definitely varies quite a bit from what's used in-country. That said, I go months without hearing "mình" uses, no matter what regional dialect I'm hearing. In my experience, "mình" is too personal and "tôi" sounds a little too crude, barely a few steps above "tao." In daily usage, I'd say names, honorifics (bà, cậu, etc), and diminutive titles (bé, nhỏ, em, etc) are used most often.