For example, if the bathroom vanity is 31 inches wide, does the countertop has be 32 inches wide or can it be the same width? I can't find any premade vanity countertop that are 32 inches wide, but the 31 size is readily available.
If this is a new house, I'd have the builder replace the cabinet.
yes, always. even if it is off center. Plumb and level the cabinet. Fasten it to the wall. place the top on. A 31' top is for a 30 or 29' cabinet.
Premade Bathroom Countertops
Run of the mill tops are usually an inch larger than the width of the vanity. A 24 in cabinet gets a 25 in top and a 30 in cabinet gets a 31 in top. Anything out of the ordinary is custom. Not a big deal with laminate tops.