Thanks, Jolan, for another great set of clues.
Here are my attempts:
1. A friend with mental illness has a craze for expressing things, initially (11
acronymania? – A crony (friend) with mental illness (mania) – gives “acronymania” “a craze for expressing things initially”. (IMHO)
2. I exit MIT exam unhappily. It’s a confused jumble (6-6)
Mixtie maxtie?- anagram of “I exit MIT exam” giving Scots word meaning “confused jumble”.
3. Trilby, possibly, set free following a record early trial (5,4)
Alpha test? – Trilby – “hat” +”set” + a LP (a record) gives “a lp ha test”, an early trial.
4. Throw one’s weight behind toboggan to leave the straight and narrow (9)
Backslide? Back- throw one’s weight behind + slide – toboggan giving “backslide” to leave the straight and narrow.
5. Words of denial in shortened form about police officer, stir men to behave recklessly (13,2,5)
Contradiction in terms? Contraction (shortened form) + police officer (DI) + “stir men” gives “ contradiction in terms” – words of denial.