Look in csx.inc, hamsandwich.inc, fun.inc, cstrike.inc and other .inc files to see what you can do. They are located in addons/amxmodx/scripting/include/
Especially look for the keyword "forward", the documentation is all there. Do NOT use the amxx api web references as they are outdated, instead use your local include files to search through what you need.
You already linked twice where all the register_event functions are at, and that page also explains the parameters you can check for the event.
"hooked_death" can be achieved with register_event MsgDeath, csx.inc's client_death and client_damage forwards, hamsandwich.inc's ham_playerkilled and ham_takedamage hooks, and im pretty sure there are other forwards you can use to detect a player's death.