Thinset tile cement.
White thinset
White or Gray Thinset would be indicated & best
Thinset mortar. There's a special one for porcelain tile; any thinset will work for regular ceramic tile.
Use a good mastic or adhesive
Can I use water & vinegar to clean porcelain plank floor tile
Use silicone .
Porcelain is usually sealed already. You then add sealer to the grout.
tile to wood? not a good idea. certainly not with adhesive. rip up the tile. it'll be worth the extra effort and expense
Yes, if the adhesive is smooth, no lumps and if you use a compatible glue, not thinset cement
A general flooring tile adhesive like Mapei Ecobond 810
A water proof tile adhesive, available at your local hardware store.
With porcelain tile you want to use a mild cleaner. Your local tile store should be able to help you choose an excellent tile cleaner. Stone Tech and Miracle Sealants make some decent tile cleaners.