Can't for the life of me get the sink & bath to stop leaking from the
wastes
underneath.

I would generally throw away the wastes that come with bathroom suites
(unless its a really expensive one). Get a decent one made out of actual
materials such metal and plastic, rather than the freebie one that cost them
20p made from God know's what.

I have used some compression hoses, as opposed to soldering on to existing
copper pipes. One has started to slightly weep. Anyone had any problems by
using these, instead of soldering ?

Tighten it more. Compression joints are perfectly reliable when correctly
assembled. If tightening makes it worse, then it was already overtightened.
Start again from scratch!

Christian.