In my opinion, if you have any kind of spider infestation on your property, then you have something else to worry about. Spiders need food to thrive, which usually means insects or other arthropods, which in turn means you have an infestation of other arthropods.
So why are you having a bug infestation in the first place? Are you leaving food crumbs all over the place? Do you have damp places where fungi and moss will grow? Insects and all kinds of critters really like those conditions. If you fix those, your insect and (consequently) spider infestation will most likely be gone.
In the case of mosquitoes, we are the food, so you can’t fix that, but you can clear out bodies of still water, which will decimate the number of mosquito larvae.
Killing them (with insecticides) only fixes the symptoms, not the root of the problem.
2. I actually like ants, unless you're talking about the really nasty ones like army ants or red fire ants. I don't mind them in my house, stealing my food; I just don't want to accidentally kill them. Some people raise them in formicariums (like aquariums, but for ants). I used to have a formicarium when I was in Canada, but have been having trouble trying to start a Carebara affinis or Carebara diversa colony in Hong Kong. Ants, like a lot of other apocrita, are actually quite "hygiene-conscient", almost to the point of OCD. Ants are also pollinators and scavengers that clean up the ground by carrying whatever they can eat into their nests. I have never heard about ants being vectors of human-affecting diseases.
TL;DR: Try not to kill the ants.