We are redoing our basement. In some areas (bathroom and laundry room) I plan on putting tile down. The basement is dry and level. Can I attach the tile directly to the basement floor?
Yes you can - and even if the floor is slightly irregular, your application of thinset can even the top layer and make it nice and solid and true.
Here's an example - my own basement (not done by me - in fact about to be removed by me - but still...)
I don't see why not.
It would be worth sealing the concrete to make it waterproof where you are going to tile, particularly as you are making a bathroom and laundry room where there'll be a high risk of water spillage.
Schluter Systems recommends using DITRA between the concrete and tile, but of course they sell DITRA, so they are not impartial.
Yes you can, I would add a modifier to the thinset (instead of water) to make it flexible and bond well.