If there was a taboo against men approaching women then there would be very few relationships. If anything, society's going towards erasing the past habit of women NOT being able to approach men. It's working towards a two-way street.

You'll never know her thought process on that unless you try to ask her out. You'll never know her age unless you ask her. Appearances can in fact be totally decieving - I've met people who I thought were older than I was but turned out they were 5+ years YOUNGER than me. I've also had people think I was much older than I am, and people who think I'm much younger than I am.

And just because she mentioned college doesn't mean she's in her first year. I was in university from the ages 20-25. None of those ages would have stopped me from dating someone who was 27.

It's not like you need to ask her out straight away either. Just try to have a slightly more substantial conversation. If you over hear her say anything about college, ask her about it.