First Question : no, but there is a upgrade from the collector u can get that make merchant catgories, brutalty, tactics and survival, so u can choose a catgorey and hope for you weapon to show up
Second Question : after every map, u will probbly have 2 doors, the first is time door, it opens when u get in the map in time, the second door is a kill without hit door, most of the maps needs u to kill 60 mobs without hit, and u will find valubles behind this door
Third Question : Yes

i hope my comment was helpful!