[noun] + 是 + [noun] [noun] + 不是 + [noun] [noun] + 是 + [noun] + 吗? [noun] + 是不是 + [noun]?
是 has one form and carries no tense. Add a time word and the same clause is about the past.
了, 着 and 过 do not attach to 是 as aspect markers. A 了 at the end of the sentence is a different thing: it marks a new situation, as in 他现在是大学生了, "he's a university student now".
Put 不 directly in front: bù shì不是.
English puts "is" before an adjective; Chinese puts 很 there. The adjective is the predicate on its own.
很 in this position is weaker than its dictionary meaning of "very". Left unstressed it barely means anything; to say "very", stress it in speech or use fēi cháng非常.
Add 吗 to a statement, or use the A-not-A form 是不是. Both take 是 or 不是 alone as an answer.
是 and 的 also bracket part of a sentence to point at when, where or how something happened. The event itself is old news; the speaker is pinning down one detail of it.
These go beyond 是 joining two nouns.
As a one-word reply, 是 means "yes" or "that's right", usually as shì de是的 or shì是ā啊.
Stressed, 是 adds emphasis rather than identity: "really", "it's true that".