the heat is only good for the first 48hrs to get the medium temp up around 35 C (95f). Past that keeping the heat on actually is detrimental to the plant.
the dome is to prevent helmet heads (when the seed casing dries out and the cotyledons can't push it off) and keep your medium moist. you should remove the dome once your sprouts are up and you see the cotys.
treating the seeds with trisodium phosphate will help prevent damping off. I imagine some weak h2o2 could help as well.