The torque converter will slip if you are on a steep hill. That's how it works, and it's a fluid coupling so there's nothing really to wear out. Probably normal.
The automatic transmission uses clutches to engage each gear, and if those start slipping the transmission might be toast. The test for it is generally to park with the bumper against a solid wall (not your garage door, please!) and quickly hit the gas until it stalls or slips. I don't recommend testing it this way because it could damage something. It can easily get to a few thousand RPM without stalling, but if the engine revs really high the transmission could be slipping. I think this would only test 1st gear slipping, so it's not a good test.
What is a slipping noise? Squeaking could be a worn belt or pulley. A slipping transmission would probably shudder or feel rough.
Moving forward after letting off the brake after coming to a (fast) stop sounds like one of the joints in the drivetrain could be sticking. If you have 4WD there are six grease fittings that you should grease (or have a shop do it). 2WD probably has three grease fittings. Even if grease doesn't fix it, it's probably normal. Coming to a stop compresses the suspension, and then letting the brake off releases the stored compression.
It could also be a sticking brake piston.
