Does my 1996 camaro have a center support bearing and where is it to replace?

its all here read it?

https://eautorepair.net/Marketing/Default.asp

I am not sure your car has a carrier bearing, but if it did it would be located on the drive shaft between the transmission and rear end of the car.

(a little late in responding - but maybe someone will need this info).

If you mean the carrier bearing on the driveshaft - then you must have a v6 model. I would advise to skip replacing it and instead purchase a 1pc shaft (no carrier bearing). The cb is located near a Hi-Speed CV Joint which make changing the carrier a little difficult.
A new replacement 1pc driveshaft costs about $225.00
The carrier bearing itself may run $40-$140. ( http://www.fortwayneclutch.com/index.php/driveshaft-parts/carrier-support-bearings/gm/1993-2002-chevy-camaro-v6-pontiac-firebird-v6-carrier-bearing-new-f-body-carrier-bearing-for-v6-models-pn-s-3r80-40.html ) - for reference...
You could also check a junk yard for a 1pc oem shaft (most shafts there are bent or have bad uj's and will cost $$ to have fixed )
>1994-2002 f-body models all have the same length from the seal of the transmission to the center of the uj @ the diff.
>when looking for an oem 1pc shaft you will find them in Steel and Aluminum. Slight differences in length when measuring center to center of the universal joints ( 40 7/8" - 40 1/2" ) - but the slip yokes vary in length, weighted / non-weighted..etc = this will make it appear the the shafts are different.
>>watch out for oem shafts with the weighted slip yoke from manual 6spd v8 models. This slip yoke may hit the trans/exhaust mount that is used on v6 models.!!

It is inside the center console

There are bearings in the rear diff that make a "whining" noise it can be repaired by replacing the bearings. Here is how its done;

1. Jack up the rear end and support if correctly with jack stands.
2. remove the wheels and expose the axles
3. remove the differential cover and drain the differential
4. rotate the main gear inside and expose the take down bolt. (8mm)
5. remove the take down pin in the spline drive. 8mm nut
6. remove the axles and remove the main gear. then take out the bearings.
7. replace the bearings and reinstall the components in reverse order.
8. refill the differential.

There are a lot of bearings back there and any of them can make a noise. If you had ground up part all of that ground up metal floating around in the oil can damage all of the bearings. Also, replacing the bearings in the differential is some very precise work and can't be done properly with out following exact specifications and tolerances. In other words you can't guess about bearing pre-load and gear tooth contact. When you take the carrier out, and also change pinion bearings you changed the relationship between the ring and pinion gears (which can also give you a noise) You have got to get a book for this car and follow the procedure and set the gears up to the given specs. You can't just replace the parts. Also, don't forget there is a bearing that supports the outboard end of the axle which can give you a noise too.

The most common reason for no reverse is a stripped or broken reaction shell. If this is the case then you will also not have 2nd and 4th. Another reason could be the thrust bearing in the front of the input drum have failed and the particals have damaged the reverse input clutches. If you are a novice I would seek professional help.

I would take it to a reliable auto center. You may have a bearing going out in the crank. Best to have it checked before your engine is destroyed.

Replace the coolant temp sensor.

Start out by checking for vacuum leaks.