My understanding is that no, they can’t, because the virus does not reproduce in mosquitos.

Similarly to HIV, it is theoretically possible for a mosquito to feed off someone with the virus then within minutes feed off someone else, be killed, and the infected blood contain enough remaining particles to cause an infection... but to my knowledge this has never been shown to happen in practice.

I’m more concerned about stray cats. It has been shown that felines can both host 2019-nCoV and get COVID-19.

I don't know enough about them to say for sure, but I haven't heard of any sort of virus being transmitted by mosquitoes. Malaria is caused by a parasite, not a virus.

Interesting question although unlikely. Certainly it's not possible with the mechanism of malaria transmission which uses a multi-species cycle.