Random power-up is definitely possible.
Jump boost can be implemented in 2 ways: Either through lowering player's personal gravity modifier (easy way), or giving them additional upwards speed boost on jump. The second option is somewhat harder to implement, but for now I think it's feasible to intercept player_jump event and find out if it belongs to player with active jump boost.
Armor pick-up which gives less than full armor is harder. Thing is, I initially planned to have several armor pick-ups - just like with health. But then I found out that I cannot modify armor amount directl