I think I'll go with this amp
How about this for a PSU?
You are very much getting into "try it and see" territory. Buying random items from Alibaba is kind of a roll the dice situation, there are no datasheets, you don't really know how well the design was implemented, and it ships directly from China, so if you have problems you are pretty much on your own.
Sometimes the devices are cheap enough that it is worth just gambling on buying 50 at once, and throwing them away if they don't work. That is up to you and your budget (both financial and time) to decide.
All the parts you have chosen are relatively easy to wire up by hand, so make a prototype and see how it works. The cable connectors are probably fiddly (is that word used as commonly in the UK as the US?) to solder bare wires to, but should be possible, then just put a lot of hot glue on the pins to keep them stable and prevent shorting. The transformer pins are large and spaced far enough apart that shouldn't be a problem at all.
Cut the outer insulation off a little section of Ethernet cable and use the twisted pairs as hook up wire; it solders pretty nicely, is already twisted in pairs, and is easy to find. It will look a bit of a mess, but you should be able to connect everything up just sitting on your bench and verify if it will do what you need.
If I were using that small amp board with input from a pro or semi-pro style mixer output, I would make a little buffer board using a decent balanced input receiver, and then either remove the pot on the amp board and replace with a fixed divider suitable for nominal pro-audio levels, or turn the pot all the way up, glue the shaft in place with some Loctite, and add fixed attenuation to the output of the buffer board.
This would probably be my go-to device for input buffer, it has everything you need except for a couple of capacitors on the input:
TI INA1651 audio receiver