Im just laying a polished black porcelain floor for a friend, using 400 x 400's, using Bal Goldstar cement based adhesive because it has porcelbond init to suit laying porcelain.
Then I'll be sealing them with Fila polished porcelain Imperg sealer once Im done, also using a flext wide joint grout, because normal grout dosen't grip to porcelain too well.
As for the level of the floor, since you need to use a 10mm notched trowel, the lines on adhesive are going to be 10mm deep, so that will give you some play with leveling them.
Use a 6ft spirit level or similar and check the level, if you only have say 4 or 5mm difference in places then the adhesive bed of 10mm will be ok to keep a decent level lay.
Hope this helps somewhat
As for a cutter, I use a Husqvarna TC670 £125, not exactly DIY equipment, and im not sure what the budget cytters are like for cutting porcelain.