No, "pants" is always plural. You need to say "a pair of pants"/"one pair of pants." "I need to buy a new pair of pants." It's also common to just say "I need to buy some new pants," which could mean one pair or several.

No. It’s just an oddity of English that pants is plural, even though the word refers to only one intact item of clothing. In some languages the word for „pants“ is a word that is in the singular, unless you are referring to more than one pair of pants.