No, a proof is bevis in that context and others.

We usually say it that way in Swedish, but in English they want the plural form. This has been quite a problem for us course-builders. For instance, in Swedish you say "Det här är mina skor", but in English they don't say "This is my shoes", and if we translate it into "These are my shoes", that doesn't work perfectly either.

In Swedish, we think like this: I am pointing to "something", therefore I think of it as "det här". It works like a formal subject, but with "här" added to make the meaning the same as with "this". In English, they don't do that. Hope this helps?

Something like De här formlerna är alla du/ni behöver för provet.

Yes, although I might be slightly more inclined to only use that in informal context.

That is also accepted.