Firstly, in the bathroom, is it better to lay the floor tiles before
fitting the toilet and hand basin, then sit them on top of the tiles?
(I have a solid floor)

Absolutely. Definitely install the tiles first. Doing it afterwards looks
like a bodge and is far more difficult, too.

I don't really want to raise the tray, so can I just chisel out the floor
to accommodate the waste pipe?

That depends on the floor construction. You may find you are digging through
the DPM, which would be a bad thing.

Christian.