I am planning to lay 12 x 12 ceramic tile in my master bathroom on the second floor and most likely I will be laying it over the existing solid sheet, non-padded vinyl flooring which is in good condition. And I will also be laying over the same vinyl flooring in my ground floor kitchen.

Can anyone provide advice on the best methods to lay over the existing vinyl and which mortars to use, especially in the second floor bathroom.

Thanks

You should not attempt to put ceramic directly on top of vinyl. A subflooring material should go down first and be nailed through the vinyl. Even if you rip out the vinyl, which is what I'd do, you still should put down a sub floor, maybe Hardibacker 1/2" sub floor.

What are the reasons for not installing over the vinyl if there are no problems with it, i.e.. Peeling, etc.

1) Vinyl is a petroleaum based product. Most mortars are water based and therefore do not bond as well.
2) Vinyl is very smooth. Mortar bonds by forming tiny hooks into the subfloor, so it is optimum to have a roughened subfloor surface.
3) Depending on the age of your house the vinyl may not be as secure as you think. Many newer sheet vinyl installations will not have glue towards the center of the floor. Usually you will have glue around the edges and staples underneath the quarter round.
4) Manufacturer warrenties are usually voided by installing directly over vinyl.

Everything Clear said is correct but vinyl also has a bit of softness to it compared to a sub floor. You can not have any movement or flex with ceramic tile and grout.

What about vinyl that is over a cement slab?

I am going to contradict muself, not the first time, and say you can tile over vinyl on cement. I was reseaching another topic and accidentally found that modified thinset is acceptable for tile on vinyl. Learn something new everyday. Try this site to verify and get more info. The bullet I refer to is about 8 down. http://www.floorstransformed.com/choosethinset.html

If you care about long term, do not tile over vinyl. Too many issues, flex, unknown quantity (e.g. you do NOT know how the vinyl is bonded) and will it break down. Bathroom floors remove vinyl, lay 1/2" hardibacker, then tile. Remove vinyl from concrete (big job) but you are guaranteed GREAT long term results.