I recently planted a purple leaf plum tree. Now it looks like it's dying. I wonder if I'm giving it too much water or too little. What do you think?

Hopefully, you bought it from a reputable nursery--was it severely root bound when you removed it from its pot? Give it some time to recover from being planted. Usually, you would water it every day for the first week and then weekly for several weeks to help it get established. You wouldn't fertilize it. If it dies, the receipt and the return of the tree would usually get you a refund.