It is firm. Firm enough to transfer energy from the ball, through the shaft, through the arms*, through the shoulders and into the body as it is rotating. We don't want any breakdown. If the grip is too lose, the club face can torque and turn and miss hits can not transfer much energy across the hands into the shaft.
Yes the last three fingers of the front hand hold the grip. If you hold the club out in front of you with only the front arm, then move your arm right and left moving the club head a couple feet, you'll feel how much grip pressure that one hand will have to apply, so the club shaft stays in line with the arm. You should feel the shaft being pulled "left" via the body's rotation. The shaft does not flip and point at the target like other instruction says. Let your body's turn pull the butt end of the shaft left as you turn through. As long as the face is square, the ball will go straight. *Both hands/wrists help hold the "setup shape" through impact.
Move Less ... Get Good! DUPLESSISGOLF