If there are loose tiles now you can expect even more tiles popping when you remove the old linoleum and the carpet if glued down. If it is put down with strip and pad the tiles on the edges will most likely go as well.
Encapsulate an old asbestos:
Asbestos should not be disturbed.....take up and re glue down is considered disturbing the material.
2 inches of concrete is more than enough,but if the tiles are loose under neath it ,a new problem is being created.
Bet it is cheaper to hire someone who is licensed to remove all the old flooring
and get a start fresh.
Most bigger shops have a Demo team. Quicker and less expensive than pouring a 2 inch cap. A good demo team can have 1000 feet up and gone in an hour.
To do a good cap the surface needs to be bead blasted (roughened up)
then a primer put down . Cant do that over a tile floor.
Wait ...you were looking for answers not more things to think about...sorry