In squash, while serving, can I drop the ball on the floor from my hand and then hit for the serve on the bounce? Or is it mandatory to release the ball from the hand and directly hit it from the racket?
No, you can't let it bounce.
No, you don't have to release it from the hand.
World Squash rules (effective at January 2019) state in section 5 The Serve,
5.7 A serve is good, if:
5.7.1 the server drops or throws the ball from a hand or racket and strikes it correctly on a first or further attempt before it touches anything else;
"Anything else" would include the ground, a wall, an object or a player. The ball can be released from on the racket, instead of the hand, if the server chooses.