1999 Honda civic EX Coupe light problem

You said you checked the fuses- did you check the fuses under the hood as well as in the passenger compartment?  If not, now's the time to do so.  Your owner's manual should clue you in to which fuses power which what.  I bet that's all it is, since the brakes and head lights are on different circuits (they don't share any switches or anything), but they both run on constant power.

Start there first, since it's unlikely that all the bulbs burned out at the same time.   What you might do is check for power at the bulb sockets and work your way back.  If you've got no power at the brake lights when your buddy steps on the brakes, check for power before and after the brake switch.  If you get nothing, chances are it's a fuse.  If you do have power, make sure you have good grounds, the bulbs are making good contact (and are not burned out), and the switches check okay.

The alarm should have nothing to do with either the brake lights or headlights.  If you have a remote start, that'll be tied into the brake lights, but would not cause it to stop working unless a fuse were to blow.

Troubleshoot the brake lights like I described earlier.

I don't believe your headlights use relays, but they are ground switched.  One easy way to see if they use relays is to turn the lights on, and pull out a relay.  If the lights stay on, put it back and move on to the next one.  If you find one that kills the lights, you know that's what it's for.

Your headlights use a 9003, which is a dual-filament bulb- one for low beams, one for high beams.  Unplug one of the bulbs and test the wires at the harness under all conditions (lights off, low beams on, high beams on), and make note of the readings.  If I remember correctly, the middle terminal is common between the two filaments, and if ground switched, should rest at a constant 12 volts.  When you switch on the lights (either low beam or high beam, you should notice one wire goes to ground).  Once you identify the wire for the high beams, the one remaining is for the low beams. 

This will help you diagnose the problem, and even if you can't figure it out, post your findings here and we'll let you know what to do next.