Expat simply is short for expatriate. A single 23 year old guy should expect a lot of going out and partying. The local women are nice, but aren't very initiative, ie. they don't make the first move.
Singapore's a small country. But there are some things you have to do to claim you've been here. Go to Sentosa, to the zoo, night safari. Eat at some hawker centre. Have some smelly stinky fruit called durian. Take the MRT train. Go to Equinox (highest club here). These are few top of my head. I'm sure there's more as you'll find out soon enough.
Where do you live around NUS? Probably in PGP cos most exchange students are there. The unluckily ones get rooms further from campus in the west. An exchange student gets orientation and stuff, I think So that's when you'll meet a lot of kids like yourself, on exchange. They usually spend the rest of the semester with one another, travelling/partying/whatever. Don't worry, exchange students have all the fun! I was on exchange before to Germany, and I really miss those times. I know how excited you must feel, I was the same!
Making friends in Singapore isn't very difficult. Singaporeans might appear unfriendly or reserved because they generally don't initiate conversation so much. However, they're more than happy to reciprocate if you smiled or say hi first.
It is NOT true that locals in NUS won't give a damn about you. I'm a student in NUS, and we always help kids on exchange.