1. I will meet him at 13:00 p.m.

2. I will meet him at 13:00.
3. I will meet him at 1:00 p.m.

(Which ones are correct? Are all correct? Where can I find the information about that on the Internet?)

3 answers

#3 is correct.

You may also say 1300 hours. You do not need the p.m. following that.
#2 is also correct (you know, after 12 midday, comes 13, 14, etc. for 1pm, 2pm, etc). #1 is not correct as it's redundent since it's understood that theh hour 13 is already 1pm. :o)
Oops I just caught myself in a typo: It's "redundant" not redundent. :o)