am: wasn't ::can:___________

aminite:constitution::________:letter
bazzar:market place::enigma:________

In your first analogy, you have two verbs; the second one is a negative contraction of the past tense of the verb. Think of it this way.
I am here. I wasn't here.
I can see it. I couldn't see it.
Using that reasoning, COULDN'T would complete the first analogy.

For your second analogy -- I couldn't find a definition for AMINITE. Please check and make sure you're spelled it correctly.

In the third analogy, bazaar and market place are synonyms. What is a synonym for ENIGMA?

Enigma

In the third analogy where "bazaar" is related to "market place", we are looking for a word that is related to "enigma". A synonym for "enigma" is "mystery". Therefore, the answer would be "mystery", as in "enigma:mystery".