Take it to auto zone and have the codes read for free.
check that the pinion nut on the differential is not slightly loose. have drive shaft balanced. check transmission and engine mounts
yes it is a rear wheel drive Automatic transmission
check harmonic balancer. check harmonic balancer.
It has 210 H.P.
No. You have to physically turn the engine clockwise by hand using the appropriate socket and wrench on the crankshaft vibration damper bolt.
There is no 5.7L engine for 2007 Suburbans
Yes, but don't tow it in drive or neutral, it will damage the transmission
Yes you can. But you will want to check you're engine soon.
Check the fluid level. If it is low, it may be slipping.
yes
It really depends on what the cause of the check engine light is.
U-joint is the first place to look. Second would be worn ring and pinion gear.