1. First-year students eat lunch at 12:30.

Question

2. First-year students eat lunch at half past 12.
3. First-year students eat lunch at half after 12.
4. First-year students eat lunch at half to 1.
5. First-year students eat lunch at half before 1.
[Are they all the same in meaning? Do we have to add p.m. at the end?]

Answer 1

1 and 2 are fine, and they mean the same thing.

I've never heard anyone use 3, 4, or 5.

You can add p.m. at the end, but you really don't need to since you are referring to lunch (and lunch is the mid-day mean).