Yes, as long as you have a left and right channel output on you record player.
#2 How can i connect a subwoofer to this soundbar, is it done by cable or wirelessly
Cable only. Unless they have a wireless sub transmitter, don't know if those exist.
#3 Can this unit be mounted to the back of a TV using universal speaker bar mounts?
This Vizio Soundbar can be mounted to the wall just under a flat screen TV. The stand feet have a hole in them where you can use a bolt to secure the bar to a wall.