I have difficulty differentiating between the 2 of them. This is a sentence I recently come across: 俺は見学でいいですか？It looks simple but I'm not sure which で is being used here. My guess is that it's the te form of nouns but in that case why is it used here? do you need to use te form to connect adjectives and nouns?
Nouns never conjugate. There is no such thing as "the te-form of a noun" in the first place. That で is a case particle because it directly follows a noun. Semantically, で like this broadly marks a condition/situation/scope, and it corresponds to various English prepositions such as in, with, by or among.
noun + で + いい is a common construction used to say "fine with [noun]" or "[noun] is acceptable".
見学 is also a suru-verb, so you cay say 見学して (the te-form of 見学する). In this specific case, 俺は見学していいですか happens to make sense, too.
EDIT: By "te-form of a noun", do you mean "te-form of だ (the copula)" explained in this answer? Then that's not the case here; this で is not interchangeable with でして or であり. This
noun + で is modifying
いい ("fine with [noun]").