If the question is, I have a laminate counter, and I want to remove the current sink /replace it with a new sink -- yes, you can do that.

Yes, but, either buy the same size sink, or one size larger, so it fits the existing hole in the formica, or the existing hole can be enlarged.

Yes, but I'd drive a wide stiff scraper between the top and the bottom of the sink flange all the way around before removal. You may chip the laminate on the way out, so a sink with a larger footprint is a good idea.

Always listen to Joseph.

Maybe he'll be wrong someday, but I haven't seen it yet.

A bath counter is SO cheap that it would be smart to consider replacing it at the same time. Then you can install the sink to the counter, and install both as a whole.

IMO if the sink is dated or damaged do the whole thing now new sink new counter honestly a new counter is not that expensive.