Recently when my brother (who got his license a month ago) drives, when he is at a stoplight and releases the clutch a little so the car won't go down when it's a bit steep, and puts into the 1st gear and gives gas (as usual to get the car moving :P) the gear sometimes pops out for no reason. This never happened when my brother first got the license, only after a couple of weeks. Did he screw up the transmission or what could be the possible problem here?

Everyonce in a blue moon this happens with mine. You're rushing things, you put the lever in first (or reverse), and when you give a bit of throttle you don't move, and you can see the lever moving and often clicking back into neutral. 

 

That being said, it's about twice or something a year with mine, and always due to my clumsyness. If it's happening more often with you, it might be mechanically related I guess.

^^ Yup, me too. Happens if the gear isn't engaged properly...

Yes, first gear can be slightly temperamental and just needs an extra notch sometimes to ensure it gets into gear.  It has happened to me before where I thought I had first gear engaged but it didn't quite slot into gear. The box has more of a tendency to slip back into neutral when in first gear compared to other gears.