if you mean merge dna with each other then that happens everyday through pregnancy, if you mean with other things then yes but it is unethically so it is not practiced
Probably not. Besides the ethical question, species are only fertile when DNA is compatible. For example, tigers and lions can reproduce to make a liger. However, because the DNA between tigers and lions are so different, ligers are infertile and cannot reproduce. The fact that tigers and lions can reproduce is only because they have some similar DNA, but most cat species cannot reproduce with each other. The closest match to a human would be a chimp, but I think the DNA would still be too different for it to work as far as mating goes.So you probably wouldn't be able to make a humanoid species.
Now, if we're getting into genetically engineering through lab equipment, I'd say that's more reasonable (not to make a new species, but to **** with nature a lot.) DNA from jellyfish was used to experiment on bunnies, and it made them glow in the dark!
We could attempt to mess with human DNA, but we'd probably just end up torturing and killing a lot of people. (But hey, what's a few bunnies in the name of science?) Also, the equipment needed for genetical engineering is very expensive. You'd need someone important on board if you want real experiments done. Which isn't very likely because of how unethical it is.