the tasks it should be able to handle are coded in C ... Each time an interrupt occurs I am pushing the following registers to stack; DPL, DPH, ACC and PSW ... or should I push more 'vital registers'
Depends on your compiler, some compilers hold certain registers as "must be preserved" others don't. E.g. if you interrupt a Keil C routine in the middle, you must either switch register bank or save the kit and kaboodle.

Erik