1) Yes I did this a year ago with about 30 sq. m of tiles, took me about 2-3 hours. You need a club hammer and a good wide bolster 50 - 75mm and a narrow cold chisel for any fiddly bits. Toolstation are cheap for this stuff. Eye protection essential, ear protection a very good idea and you may want to wear a mask. Get the bolster at a shallow enough angle and most should lift with ease. Your floorer will proably put down leveling solution to cover the mess of tile adhesive which will remain but try to get rid of the worst of it with the hammer and chisel.
2) A second clean may get the last of it out, wait until the carpets are thoroughly dry before passing judgement. Or: