Yes. But as is the rule with anything, prep is key. You shouldn't be thinking about putting tile over the vinyl. It's a lot more work than that. Most likely, the vinyl and the wood it is glued onto will need to be removed. Then you will put down backer board, make sure it is all level. The tile will go on top of this. The basic reason you don't tile over the vinyl is because the tile may be adhered to the vinyl completely but since you don't know that the vinyl is 100% covered with glue on the back and is 100% attached to the floor below it then it can pop and the grout will crack. I guess another way to describe it is that the tile is only as strong as the weakest spot of adhesion. (vinyl adhesive is usually not spread out all over the product, but rather it is randomly placed) You will also need to verify that the floor is strong enough for tile. You should head over to a tile forum and get some help from people who can explain all this to you better. Bill_V is a great resource. There is also a non GW site but for some reason if we mention it here it raises a red flag. Google John Bridge and see if you can find help there. I think Bill V is often found over there.

Not yet, though it's only been 8 months that we've had the tile. Maybe it's mind over matter: we love our tile! :) We also aren't cruising around barefoot all the time, and I don't do a lot of standing in one spot for extended periods. I've often heard the issues that you mentioned, but I sometimes wonder if part of the problems aren't due to individuals' poor posture, sinks/faucets/cooktops not being properly positioned (i.e., too far forward), etc. My elderly mom complained of her hard floors starting to bother her legs, so I picked up a couple of those foam floor mats -- she finds them very cushy, and they've helped greatly.

Not a pro, but if you insist on same-day, you could end up skewing your carefully-placed tile by not letting it cure fully before proceeding. That said, you could check with Laticrete to see what they have. Laticrete has some very tech-forward products that might offer what you want. They have a good customer service phone line you can call for help, and you can also peruse the website for different offerings they have. If you end up going with Mapei, get the pre-sealed grout for ease of cleaining.

You can paint the tiles. Not a problem. Tile paint will hold up for a year...maybe a bit longer. Then it starts to wear through...looking more rustic with every month. Worst case scenario you HATE it and redo the floors. Best case scenario you can create a 'down and out damaged rustic look floor' without breaking a sweat....'cause that's what you are after in the first place. When do you think you will get around to a FULL kitchen renovation?