1.) What type of pest control products to you use as a barrier to insects for both your house and lawn?
Well, we started shutting doors to the house after a bufo invited itself in to watch a little TV with my spouse. It does a better job of pest control when it's outside the house.
We let the spiders live as long as they don't set up housekeeping in the high-traffic areas. Cane spiders, of course, get the cardboard & glass jar treatment and are swiftly escorted back into the yard. Scorpions (yes, Hawaii has small brown scorpions), cockroaches, and centipedes are killed on sight with a size 9 rubber slipper. We run the water jets in the whirlpool tub at least monthly to discourage ants from setting up housekeeping in there. I don't want to talk about how we learned that we needed to do that.
We cover our vermipost with a thick layer of newspaper to discourage the fruit flies, but we also have several anole and geckos living happily on the back lanai.
The best way to discourage ants & cockroaches is to not make a mess, or clean it up as it happens. The second-best way is to spray their entry point (window vents, door thresholds) with vinegar to destroy their scent trails.
I've killed a lot of ants with diatomaceous eath or with borax powder, mixed 5% with sugar water or grease/fat. The little black ants prefer sweet while the bigger ones like the grease. Pets & small children might be tempted by the bait, so it's best to use it outside on the ant trails.
We just had a persistent invasion of carpenter ants and some smaller cousins. They thought the borax was yummy (and it killed a lot of them) but it just seemed to be attracting the entire nest to move indoors. Ant bait traps (using fipronil) didn't seem very effective either. I finally used a spray bottle of Terro's Carpenter Ant & Termite Killer and wow-- four days later the ants are still staggering out from the nooks & crannies to die on the floors. It uses deltamethrin, which seems to be the neutron bomb of ant neurotoxins. I just sprayed a mist on the ground outside one door and on top of another nest inside a lava rock wall. But at this rate it'll take me at least five years to use the one-quart spray bottle.
Our lawn is a combination of Bermuda grass, St. Augustine, and El Toro Zoysia IV. About the only thing they seem to need is a good soaking every 4-5 days. We've never needed to spray any pest chemicals on them, and over the last decade we've thrown out all our traditional lawn poisons. I kill haole koa trees and nut grass with RoundUp spray.
2.) Any recommendations for products to fertilize the lawn and keep it green/healthy/weed-free?
We don't use any fertilizer either. If our fruit trees get any more productive then we'd be feeding an entire block of neighbors, and most of them already won't answer my e-mails or doorbell ringing...