My GE washing machine WWA8360GAL is noisy when water is filling the tub and used to screech when going into the spin cycle. Now it goes into the spin cycle only intermittantly, however the water will drain from the tub. Watched it operate with the back cover removed and noticed:
1) there is a very slight leak at the pump drive plate (upper part of flex coupling) only noticeable when water is filling the tub (when drive plate is not spinning).
2) The drive belt is loose (about 1" deflection) and appears to be breaking up (bits of drive belt can be seen on back cover and motor mount).
3) Flex coupling has separated in one location at connection with pump drive plate, but motor, coupling, and pump drive plate did all rotate. For the test run that I witnessed, the unit did go into the spin cycle.

I'm planning to replace the belt and flex coupling. Should I inspect pump further or just replace? Do I need to inspect the clutch bearing as well?

Quite honestly.. I would disconnect the machine and give it a complete overhaul before you use it again.

Water an electrics ring alarm bells.