Demolition/removal should be included in your fabricator's estimate.

It depends. DH and I did all the demo for our kitchen remodel (we were able to repurpose almost all of the old cabinets). We also did the demo when we got new shingles on the house (with the help of our 2 teenage kids). We had the roofing company bid the job with and without demo, so we knew how much we were saving by doing it ourselves.

Ceramic tile removal would be tedious and require a fair amount of manual labor, but if can certainly be done. Oh yeah, we removed the ceramic tile from our foyer when we got new flooring (I guess we like taking things apart :))

Whomever you pay to do it. No one includes a tile counter demolition ever. That’s a huge pain, and runs around $10-$20 a foot to demo. Because you have to be careful doing it to not damage the cabinets. Plus the needed dust control, debris disposal, and timing it all correctly.