Noise

So you can only hear it when its in gear when cold?No other time?

Backing up in reverse you will hear a whine because the reverse gear is straight cut. So can you hear this noise in every gear going forward or a certain gear?Is it only heard while pressing the gas?

Alright now that you have better described your problem if it makes a single pop or thump noise while backing up or turning I would suspect one of the lower control arm bolts are loose that hold it on to the subframe doesnt take much looseness to cause that. But if its only while cold and turning the wheel I would say you have a bad upper motor mount that is located by your valve cover its common for those to go bad on those cars. See if it looks colasped or torn or both it should be easy to see if its as bad as you describe. Also the lower transmissiin mounts colaspe and tear loose from its metal base. There especaily noticable when in drive at a stop
Its located underneath the transmission between the transmission and subframe. If you look under the car from the passenger side towards the drivers side you can see it if its pretty thick its good. If it looks thin and colasped its bad. Another thing you can do is go to a auto parts store and compare the mounts to new ones. With the upper mount they have two styles one has a wider rail at the top of the mount and the other one has a narrower rail at the top of the mount. You want to replace the mount with the narrower top rail. Let me know on this posted question what you find.