Can you lay self stick vinyl floor tiles over old sheet vinyl flooring

yes

You can lay it on top, but make sure this would only be the second layer. ALSO.make sure the floor is SUPER clean. I did this and it worked out fine, except for 1 little speck, that caused a bump underneath the new stuff.

Can be done but the surface should be clean

u can lay it over the old linoleum as long as the seface is cleaned, dry & free of residues like wax. the manufacturer will specify if u need any additional glues on these surfaces, but most do not require it. it is better to start with a new floor, but not neccessary. just make sure ur seems r good & not too tight. & i've laid four of these over existing linoleum & my only trouble was some buckling (the tiles coming up together at the seems because they expanded & could not fit right) so i would suggest keeping the tiles stored in the room u want them in for at least 3 days to acclimate to the temp of the room & even though u want to make sure u have a tight seem, do not push them too hard together, so the had a little wiggle room for fluctating temperatures. & in a bathroom, make sure to caulk around all fixtures when ur done.

No, you do not have to take up the old vinyl. Just buy some Luan (very thin plywood) and nail that to the existing floor and when you are finished with that, make sure that the floor is absolutely clean before setting the new tile.