You have two seperate issues.
#1 You need to adjust your shifting rod to get it to go into reverese. When the service people had the lower unit off they probably altered the length of the shifting rod hence the motor not going into reverse. It requires you to drop the lower unit everytime you screw in or out the shifting rod (PIA). The rod can be measured for the distance and it will get you very close. I dont remember off the top of my head the distance but I can get back to you on the length.
#2 Your trim motor could be the problem or it could be the electrical portion. Remove the cowling and listen for a click when you push the trim control. No click could mean you have a bad selinoid and would likely affect the up and down and not just one direction. Check to see if the unit has ATF fluid in the reservoir, fill purge air and try again. Do you hear the motor working when you push the trim button? if so Its likely fluid problem. If the selinoid is good and you have fluid in the res. Then its likely the T/T motor. They are rebuildable but I would buy another one, they are around $60.
If you need to lower the motor you can turn the manual release valve and it will allow the motor to do down. Be advised if this valve has not been turned in some time they can be very difficult to get unstuck. If difficult, soak the area down with PB blaster or Aerokroil and wat a few hours and try again. If you really crank on the screwdriver you will likely damage the slot where the screwdriver slot is.
good luck