Does the motor have to come out in order to swap the transmission?

On most GM front-wheel-drive cars, the engine cradle, (cross member) is dropped out the bottom after the upper strut mounts, fuel lines, exhaust pipe, and wire harnesses are disconnected. The engine and transmission come down with it. That makes the job a little easier but there is one very important thing to watch for. When the cradle is bolted back in place, it can be shifted sideways. That will move the bottoms of the wheels and severely affect the alignment and handling. The affected alignment angle, (camber) can often be corrected with an alignment, but if you don't tell the mechanic about having the cradle out, he will likely overlook "steering axis inclination", (SAI). When that is not equal side-to-side, you'll still have real miserable handling even though the alignment appears to be correct. To avoid that problem and the need for an alignment, use spray paint to make "witness marks" around the four cross member rubber inserts. With those paint marks, you'll be able to position the cradle exactly as it came out.

Just to add to this one Yes the cradle would come down you would drop the exhaust down pipe off seperate the ball joints remove the side covers behind the wheels the lower splsh gaurd etc. Also below the radiator there is a wire loom hold down unsnap that as well as the o2 sensor wire hold down back by the rack and pion. Also by the rack and pion there is a small thin metal tube cliped to the cradle. As far as dropping the engine and cradle together no you not going to do that. You will get a engine support to support the engine then it will be safe to drop the craddle. When you put the cradle back in leave the cradle a little loose. Then by the cradle bolts by the radiator you will see some round holes by the bolts I take a long 3/8" drive extension in those holes to align the hole in the craddle with the hole in the frame of the car. That will get you close but you will still need a alignment. As far as the shifter getting loose inside the car suddenly the most common reason is the black outside connector on the shift cable that connects the cable to the base of the inside shifter breaks. Have you moved the inside shifter and watched to see the cables on the transmission are actually moving?I would hate to have you pull the transmission for nothing because of a bad cable.I also have info on repairing the black cable end if its broken. Let me know what you find.