Mosquitoes – yes.
Noise – no.
Noise, ie Sound, is just pressure waves moving through the air. So if the air can come it, so can the sound. You can soundproof a room and have the air moved through ducts and such that create distance from the sound source and thereby make it harder to hear….but this doesn’t seem to be what you’re asking.
I love having my windows open. I got the heavy duty screens because I had bird nesting nearby that took my older lighter weight screens and would tear holes in them to use in their nests. No bird has made a dent in my heavy duty screens.