Yeah, it should be a short vowel. :)
Why can't we say mina olen jano?
jano must be used with the subject in the adessive case.
Read: “I have hunger.” You are not hunger itself! :P
Why is I minulla in this sentence. Minulla is I have..... Mina is I am
Because in Finnish thirst is something one has, therefore I am = Minulla on. It's also possible to say Olen janoinen but it's less common.