I would think so, but check the specs for your sink to be sure. It has to fit within your vanity. 21" vanity is pretty standard.

You should have no problem with that.. the interior of your cabinet should be about 19 1/2" -so the sink and faucet will fit fine... do some math with the thickness of your backsplash and what ever the base size is for the faucet just to be sure....

This is tight and may not work, assuming this is an under mount sink with deck-mounted faucets.

By depth, I'm assuming you mean the distance from the front of the sink to the back of the sink, and not the height of the sink. Some web sites refer to this measurement as the "length" of the sink.

How much overhang (distance that countertop extends horizontally beyond the front edge of the cabinet) will you have on the countertop? I have 1/4" overhang in one bathroom and 1" overhang in the other. How thick is your backsplash?

Standard space from front edge of sink to front edge of countertop is 3.5" (assuming countertop is not small tile). Standard deck-mounted faucet holes are 2.5" in diameter. Recommendation is at least 5" distance from back of sink to backsplash, but 4" may be OK.

Assuming: 14-3/8"-deep under-mount sink; 1/2" overhang of countertop around sink (leaves 13-7/8"-deep opening for sink); 21"-deep cabinet extended with 1/4" overhang of countertop at front edge; subtract 1" for backsplash. This allows 3.5" of countertop in front of sink and only about 3" behind the sink (distance from back edge of sink to the backsplash).