I am having some troubles with the extruder at the beggining of the printing process. Is not extruding well but then it just works fine, also the Z axis stop working after a while.

Are you priming the hotend before the print? Running a brim or a couple of loops should solve that problem.
For the Z axis are you activity cooling your electonics?
Might help to share your machine type and what type of hotend.