I planted two apples as well as some other fruits trees in around October. They're both about 2yrs old as well. So Im pretty much on the same boat as you. One Golden Delicious and one Honeycrisp. The golden came potted and leafed out while the honeycrisp came bare root and leafless. They are both doing terrific and I wasn't expecting fruit for awhile either really. Although I should've after doing some research. I got a cluster of 5 apples on my Golden Delicious. Only one remains though.

But to answer you question about taking your fruit off, I wondered the same thing but then again I only have one apple. So I'm curious to hear what others say. Id guess you could keep a few maybe because you don't wan't to much weight and stress on such a small tree. But I'm no expert.

Then, with the lower branches on your red delicious.. If they're coming out of the rootstock definitely prune them off. And I cut off any branches that were lower then I think a foot and maybe a half? up the tree.