Learn English – What do you call someone who attends the same university as you

I think you can use a night owl, or a night-person.

I think a sleepless man is fine. Another similar word is an insomniac (a person who suffers from insomnia), but I believe that you know it already.

Actually, what you describe sounds pretty much like me myself. :)

Sometimes, people called me a vampire, a batman, or a dark knight, which is not quite to my taste. In casual chatting, I personally prefer a night dweller or a man of the night more.

Here is an excerpt from Wikipedia's page Night owl:

A night owl or evening person is a person who tends to stay up until late at night. The opposite of a night owl is an early bird, a lark as opposed to owl, someone who tends to begin sleeping at a time that is considered early and also wakes early.

(AmE) I don't use or hear "agemate" or "batchmate". I might understand what you mean by "agemate", but definitely not "batchmate". Personally, "batchmate" sounds like computer programming jargon.

If it interests you, please consider the following expressions.

1. We are the same age.

This does not imply that we were born on the same day in the same year. It doesn't even imply we were born in the same month. I think most would agree that it implies that we're are about, at most one year apart. For example, we are both 25 years old.

2. We are both X years old.

This is pretty clear: we've been alive for (at least) X years. Maybe I am closer to 26, and the other person just turned 25, but we are both 25 years old.

3. We're about the same age.

This is bit ambiguous, but I think you can certainly use it if two of you are about 2 or 3 years apart in age.

4. We are X years apart.
5. We were born X years apart.

4 means that the difference between my age and another person's age is X years. 5 might be used by siblings.

As others have mentioned regarding your other requests, you might consider contemporaries and classmates.

In college and high school, students are often called

6. Freshman (plural, freshmen; first year student)
   We're freshmen!
7. Sophomore(s) (second year student)
8. Junior(s) (third year student)
9. Senior(s) (fourth year student)

In college, students are also called first/second/third/fourth/etc-year students. Sometimes, the word student(s) is omitted.

10. We're first-year students!
11. We're first-years!