It is certainly ok to use bleach. No need to dilute it first. You can either pour it in front of a return jet or directly into the skimmer while the pump is running which is what I do. (By the way, if you ever have a need to shock the pool, turn your SWCG off and just use bleach to do so. Using the SWCG on the superchlorinate setting simply ages your cell faster and limits the life of it.)

I'll let someone else advise you on your specific questions about your unit.