Basement Bath floor

I would most definitely take up the linoleum. Why? If it starts coming away from the floor substrate (particle board), it could then very well lead to the grout between the tiles cracking (breaking up) due to movement underneath.

Personally I have no time for particle board, therefore would be very! tempted to take it up and replace it with plywood (fixed down appropriately).

That said, according to Schluter-DITRA and Schluter-DITRA-XL: Wood Substrates you can probably get away with keeping the particle board down on the floor. Before commencing I would ensure the particle board is fixed down very! firmly (nailed or screwed @ 150 to 200mm centres). Select a nail or screw length that will not go all the way through the floor boards underneath the particle board, you don't want to go hitting any pipe or cable that might run underneath your flooring.

For total peace of mind I would contact Schluter Systems directly and seek their advice: Contact Schluter Systems

The floor does not have to be perfectly level. Just flat enough so the flooring lays flat. I use a 4' level or 2x4 and check the area. You dont want the level to teader or have a gap under it more than 1/4"-3/8". Small trouble areas you can fix with doubling up on the underlayment.

If you need to level the floor more use floor leveler let it set up then drag drainage grooves towards the drain. Using a screwdriver will be the best width. Thicker would be better but it will mess up the surrounding concrete. You will want to remove the old floor drain set it at the height you want the new concrete to be. Once the concrete sets up you can drill or cut some notches where you put the drain grooves. Doing it any other way may cause you to fill your drain with concrete.

You can also cut drainage grooves once the concrete has dried. I would use a circular saw or grinder with a mason blade. But this will not leave a thick groove and trying to make it wider would be time consuming. If you were to do this i would would suggest cutting 2 lines about 1/2- 1" apart. then take a chisel and break out the area in between.