99 Olds alero will only turn to the right. On quick inspection found that the rack and pinion moves with turning the wheels. Is it supposed to?

yes you possibly can ( depends on the room available.)
I would do the centring at the top of the rack and pinion as this is where a multi spline is that will allow for correct centring.
when you get the shaft off the box
firstly turn the rack from lock to lock ( wheels of the ground) and position the shaft at the midpoint of the turns counted fro left to right
next with the steering wheel place it in the straight ahead position
put the shaft back on the rack and tighten up the lock bolt

The most common of all problems in a steering system is excessive steering wheel play. Steering wheel play is normally caused by worn ball sockets, worn idler arm, or too much clearance in the steering gearbox. Typically, you shou Id not be able to turn the steering wheel more than 1 1/ 2 inches without causing the front wheels to move. If the steering wheel rotates excessively, a serious steering problem exists.

An effective way to check for play in the steering linkage or rack-and-pinion mechanism is by the dry-park test. With the full weight of the vehicle on the front wheels, have someone move the steering wheel from side to side while you examine the steering system for looseness. Start your inspection at the steering column shaft and work your way to the tie-rod ends. Ensure that the movement of one component causes an equal amount of movement of the adjoining component.

Watch for ball studs that wiggle in their sockets. With a rack-and-pinion steering system, squeeze the rubber boots and feel the inner tie rod to detect wear. If the tie rod moves sideways in relation to the rack, the socket is worn and should be replaced.

Another way of inspecting the steering system involves moving the steering components and front wheel BY HAND. With the steering wheel locked, raise the vehicle and place it on jack stands. Then force the front wheels right and left while checking for component looseness.

Disconnect the column from the rack & pinion, And then see if the wheel will rotate left. If it does, then it IS the rack & pinion or some thing is jamming it. That is a classic sign of a bad rack & pinion. It takes more hydraulic pressure to turn left than to the right, and the and so the floating ball hits the seal harder, and wears it out faster. Then the pressure just returns to the pump in stead of moving the tires left.

NOTE: DO NOT turn the steering wheel more than it does when connected the the rack & pinion.
For this test one turn either way from center will suffice. If you turn it more, or fast, you will probably break the "clocking spring" inside the steering wheel. Then the air-bag warning light will come on. The spring tells the air-bag when its safe to fire the bag in relation to the wheels position.

Hope this helps.

RETURN TURN LINE GOES TO THE LEFT OF RACK PINION AND HIGH PRESSURE HOSE GOES TO THE RIGHT OF RACK PINION.LOOKING AT POWER STEERING PUMP HIGH PRESSURE HOSE THICK HOSE SCREWS INTO POWER STEERING PUMP.WHILE LOW PRESSURE HOSE HAS A HOSE WITH A CLAMP THE LOW PRESSURE HOSE HOOKS TO TOP OF POWER STEERING PUMP.LOW PRESSURE DONT SCREW INTO POWER STEERING PUMP IT IS HELD IN PLACE BY A HOSE SMALL CLAMP.

CHECK POWER STEERING PUMP PRESSURE LINE GOING TO RACK AND PINION. ITS MORE LIKELY THE LEAKING LINE.

This could be a few things, I would first start by having the front tires inspected and balanced. Unbalanced tires or a tire with a broken belt can cause both a sway and a vibration.
If the tires check out then the only components left are the Rack and the tie rods. If you already have a leak in the Rack you are not long from having to replace it.
You can test the rack and pinion yourself with the help of another person.
Have a friend sit in the driver seat to operate the wheel. (Do Not start the car)
Leave the car on the ground so that the wheels have friction against the ground. You can sit next to the passenger side, have you helper turn the wheel all the way to the left. You will now be able to see the tie rod end and Rack arm. Now have the helper turn the wheel slowly to the right. You will be looking for how much movement is in the arm and the tie rod end before the wheel tire starts to move. You might also see the tie rod end move up or down or hear a slight popping sound. Any of these is an indication that you need Tie Rod ends.
Repeat this process on the drivers side noting any movement of parts prior to the tire moving.
If all the parts are good as soon as your helper turns the wheel you should see the tire move immediately.
If you notice that you see a delayed movement from the time you turn the wheel and the time the Rack Starts moving then you will need to replace the Rack.
Thanks, and I hope this help. Dorrian

seems like the pressure line to the rack&pinion is plugged.open the line at the rack see if fluid flows if not replace line if fluid flows then replace the rack.

I'm not sure if that truck has rack and pinion steering, or a steering sector. In either case, it sounds like you have stuck valve and the hydraulic pressure is fighting you, instead of helping you. When ever you turn the steering wheel the valve is supposed to move and direct the hydraulic oil pressure to help you steer. The valve is built into the sector or the rack and pinion, you may have to replace the assembly. There are companies that recondition those items so you might want to shop around.

did you hit anything?you might have bent the rack and pinion tie rod ends (inner) or you might have broken the attaching bolts to the rack itself.

If it is hard to turn it could be the fluid is low. If you can't turn the steering wheel go underneath the lower rack and pinion right were the steering shaft bolts to the rack and pinion there should be a round silver cap looks like a plug if that cap is missing the pinion bearings are broken and the rack and pinion are locked up replace your rack and pinion