The makers of Allure vinyl planks say their product is suitable for basements where moisture is controlled. Tile on concrete is cold indeed. You'll probably want to put area rugs on top. Older concrete basement floors were often only a couple of inches thick with no gravel or vapour barriers underneath and no mesh reinforcement in the concrete. So you'll want to check for excessive moisture and definitely use an uncoupling membrane such as Ditra under ceramic tiles.

It's really a matter of how well the adhered tiles are stuck. If you can get something like one of those roofing tear up bars underneath and pop the tiles up in full pieces, you aren't likely to generate much asbestos dust. The adhesive can have asbestos also so it could be wet scraped and picked up with a wet vac with a capture bag. If the tiles are adhered such that they break into little pieces, you can likely float where the loose tiles came up and put a new floor over the top. There's also floating vinyl floors that sound like an ideal solution for your situation but I know little about the efficacy or quality of these products.

https://www.flooranddecor.com/porcelain-tile/truewood-cream-wood-plank-porcelain-tile-100480698.html#srule=Price+Low+to+High2&sz=120&showBrand=true&start=1 There is also this one at about 1/2 the price. https://www.flooranddecor.com/porcelain-tile/bradford-natural-wood-plank-porcelain-tile-100503457.html#srule=Price+Low+to+High2&sz=120&showBrand=true&start=43

No problem...remember the real Saltillo needs waxing/polishing to REALLY show them off. The glossy Saltillo tiles show off their colours. Just make sure you get the maintenance 'stuff' as soon as you have the tiles installed. You can practice with a few left over tiles to get the hang of it. The Saltillo will out live the house! I like the highly coloured ones (with the strong dark oranges mixed in with the light sandy ones) but it is your home. Make sure you get what you like!