Not really a job for a DIYer
Drilling a hole in tile with a diamond hole saw: make a moat from putty to keep a pool of cooling water round the bit.
Diamond jigsaw blade needs water cooling when cutting tile
Heat vinyl floor tiles with a torch to soften them. Easier to make awkward cuts and can bend them to fit round pipes with a single cut rather than removing a slot from the tile.
First tile goes in the centre to minimise error accumulation.
Peel individual pieces off mosaic tile backing, cut them and then put them back on the backing
Remove grout with a grout saw and then hoover it out
Add anti-fracture membrane before laying floor tiles - roll on liquid type is easiest.
Back butter portions of floor tiles that are uneven