For the targeting thing, I come across that same issue as well as the opposite.
It's like when I don't want to target mine or someone else's summon I do, but when I want to to heal them I can't >_>;

To get rid of the pet hotbar:
System >> Character Configuration >> Hot Bar Settings >> Cross >> Untick 'Use pet hotbar.'

What I'm trying to figure out is how to keep the pet hotbar active while still being able to have access to my main tab and the R1 quick tab.
I want to be able to command my pet every once in a while but still have my abilities mapped on the cross hotbar but I'm finding it difficult to setting that up >_>;