Tile adhesive will set better on a cold rather than hot surface. The coolness of the surface allows the thinset not to dry out before it has a chance to bond. Be sure to keep the tile, thinset and surface temperature between 45 and 70 F for at least 12 hours.
A toilet in places where no drain lines exist is still possible. New toilets that flush up solve the problem. These up flush toilets can be installed in spots that were considered impractical in the past.
Is your current plastic laminate top scratched and possibly sporting a couple of burn marks? If it is a square-edged top, it is possible to apply ceramic tile right on the laminate. The toughest part of the job is simply dealing with the sink. You can do this job!