Hi Breexy,
This year no fruit,but should have some next and more in succeeding years.
It can be pruned anytime during the summer,maybe wait about a month and how much is your choice.Pruning is for shape and to let light and air circulation in the branches.Try to keep the center open.
Did it come in a pot or bare root?What kind of Plum?Thanks, Brady

It came in a pot. It looks like it is red plum (i still have the tag, which says "plum red"). Is there anything I can do now to better care for it?

It's probably an Asian plum. It should do well where you are.

Looks to me like it's already established a central leader, not an open center. That's OK, but prune out all branches facing inward to keep air circulating in the center.

Alright, will do ltilton.

What about fertilizer? what kind would be best for it? should i fertilize it at all?

It might be a little late to start fertilizing now.A balanced one,like 10-10-10 will work and can be applied once a month, April-July,about 8 oz.for each year of tree age.Spread it around the drip line.Less is better than too much when fertilizing. Brady

Nitrogen fertilizer will produce vegetative growth, lots of leaves, but too much can inhibit fruiting when the tree comes of bearing age.

Some people don't fertilize fruit trees at all, but it really depends on the condition of your soil how much you need, and what kind.