I have mosquitoes but no more than any other area. Weeping willows
prefer wet soil and so do mosquitoes, so where you you find weeping willows
you are going to find more mosquitoes usually, but weeping willows
do not cause mosquitoes.
It is fine and even recommended to feed birds year round. It makes the parent birds' job much more easier to feed the babies, if you provide a steady and abundant source of food for them. Also I use an old suet cage and stuff it with dryer lint and wisps of hair (my hair is down to my waist although I am a 53 year old Male). I hang this with my feeders and the birds take the material to help build their nests. Also provide a bird bath for drinking and bathing. You should soon be overrun weith birds of many species. I even have Great Blue Herons and Canada Geese fly over from time to time and I live 5 miles from the closest large body of water.