Is it moral to kill a mosquito? The moral angle on this question doesn’t get sufficient exposure if we limit it to mosquitoes. Morality must extend beyond that. So the question becomes more about killing in general and not killing of a specific species of creature.
I think killing is inevitable. Millions of germs die every time we sneeze. Our entire body is composed of cellular life that dies and is reborn day in and day out. The whole food chain is a cycle of killing and being killed. This is the way of life. While the fate of individual animals or species may suffer in the short term, life as a whole, lives on by feeding on itself.
Human beings have these ideas about morality that keep them at a distance from the rest of nature and the universe. This whole question dissolves into nothing the moment we realise we are not the ones making any decisions about right and wrong.
Having said that, there is a very real gulf between nature and culture. It exists because human beings acknowledged it as being the deciding factor between extinction and evolutionary advantage. It is not surprising therefore, that our ideas of right and wrong — which are efficient when deciding the way we behave with other human beings — often get applied to subjects like the morality of killing a mosquito.