I was in an accident. An insurance adjuster seemed friendly, told me he was "on my side" and offered a fast settlement. Should I accept it?

Not before consulting with your lawyer.  The truth is that insurance adjusters are not on your side as they work for the insurance company, not you.  Insurance companies are in business to make a profit.  The less they pay you, the higher their profits.

After an accident, the person truly on your side fighting to get you the best recovery is your lawyer.  Your lawyer will tell you all the different things you are entitled to receive money for and thus the true value of your claim.  Because of this, you should never accept a settlement offer from an inusrance adjuster without first consulting your lawyer.