The most important issue you have listed is the problem with the "joint filler". This is actually the mortar that holds the block together. It sounds like you will need to have this "retucked" or some call it tuckpointing. This is where a mason would come in and replace this mortar to make the block structurally sound again. No, you can not put joint compound over it.
I'll let others cover your other questions.
Good Luck!
Dodgeman