When gear is put in reverse it makes a squeeling sound but just in that gear.

the "backlash" felt by reversing the drive shaft direction is normally the clearance in the spider gears in the diff so to get rid off that ( not necessary unless it is excessive) is to pull the diff center out and fit new thrust washers behind the spider gears
next check the diff mount bushes as the diff reaction will move the bolts in the mounts and make the noise

try bleeding the slave cylinder sounds like the clutch is not disengaging enough to slow the transmission down enough to allow it it to fall into gear

REAR BRKS HANGING UP

Transmission needs repair and service.

It sounds like the reverse band broke. Typically with automatic transmission when you put the transmission in reverse a couple things happen. Usually, the forward clutch engages and the reverse band engages holding the reverse drum from turning, which causes the planetery gears to make the vehicle move backwards. If the band breaks there is nothing told hold that drum from turning and you have a forward gear. The bad news is the trany is going to have to come out to be repaired and usually the reverse drum is one of the first things to go into the trany, so it has to be completely disassembled. Take it to a transmission shop have them check it, hopefully it's something simpler.

YOU MIGHT HAVE ONE OF THE LINES ON WRONG. REVERSE THEM

check the transmission fluid, make sure its at the proper level, look for correct reddish colour also check for burnt smell

SOUND LIKE THE DAMAGE INTERNAL GEARS IN TRANSMISSION LOCKED UP LIKE THE PLANET PINION GEAR AND SUN HAS FAIL LOCK UP IF.THESE GEARS FAILED THEY WILL CAUSE ENGINE TURN OFF IN REVERSE.ALSO CHECK TRANNY FLUID MAKE SURE ITS NOT TOO LOW.

if you are only having the issue in reverse that would make me lean more towards the transmission having an issue than the clutch.

when they put the new pads on they should have sprayed them with permatex anti sqeal a lot of techs are lazy and the dont do it bring it back and complain they will spray them