Re: Catch up on something or with something?
Give a context please! How do you want to use it?
Is there a car in front of you do? Do you want to pull even with it? You want to catch up with that car.
Do you have a favorite television show? Did you miss the last few episodes? You want to catch up on your television series.
It doesn't matter whether it's a thing or a person - it depends on the meaning you want to convey!
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.