Walking off when mounting will become worse if it is not corrected soon. It depends on the horse for the solution. If he is a nervous type, then practice approaching, then back away without mounting several times until he is okay with it. Then flap the stirrups around until that's good. Place a foot in the stirrup, or even just raise your leg, and just practice all the parts to mounting separately without mounting untilhe is okay with it. Or, you might try doing some groundwork exercises to help him to think and not react. If he is a lazier type, then I would make him work on the ground, and rest near you for him to realize that it is easier to hold still than to be silly.
Turning and biting when asking for a trot could be either a respect issue, or a pain issue. If he has just recently started doing this or does it at a walk also, it is likely a pain issue. If not, then one would assume it to be a respect issue. When he turns to bite, bump him with your foot to make it uncomfortable. Do it hard enough that it won't happen again, not just push him away. Keep pressing and asking him to move forward, and steadily increase the pressure. If he still refuses to move, spank him with a crop or a spanker, immediately release all pressure once he begins trotting. However, don't release until he trots, keep spanking if necessary.
If you look for truth, you may find comfort in the end; if you look for comfort, you will not get either comfort or truth; only soft soap and wishful thinking to begin, and in the end, despair. -C.S. Lewis