How safe are household insecticides for humans?

And are they natural alternatives I can use to kill ants and roaches?

Here is my answer based on my experience of living in an apartment where no amount of chemicals, poison, boric acid, or whatever would get rid of them. Here is how I did it.

The key is using caulk to seal up all the places that roaches like to nest. These places are always near water, like the kitchen or bathroom. The most likely places are the cracks between the floor and the baseboard moulding on the wall, and at the top of that same moulding. Seal it up everywhere. If your roach problem is bad enough you may have to go around the entire room.

Next is the long crack where your kitchen counters meet the wall, especially near the sink. Roaches like to nest where it is dark and where there is very little headroom above them, so the space between the kitchen counters and the wall is paradise.

There is a way to use boric acid without danger to your loved ones. If you find cracks to seal at the baseboards, before you seal them, you can brush some boric acid through the crack before sealing it. Likewise, you can put some behind the counter before sealing it up. Boric acid does work great. It is not a poison, so roaches cannot become resistant to it. Instead, when the powder gets on them they ingest it when they clean themselves, then it swells up in their stomachs and kills them when they drink.

The key is sealing everything up. After that you can place small amounts of the various poisons and traps to kill the roaches that are still there, i.e. the ones that now have no place to nest but are still hanging around.

If you believe that you have sealed everything up and still see roaches, then you have missed something. If you see a roach, instead of killing it, just follow it to see where it goes. Then seal up that spot. If you can't seal that spot then place a small amount of poison there. (There is a small tube of roach food poison sold that is good for that.)

Finally, if you have sealed everything up and still have roaches, do you have carpeting near the problem? The roaches can nest under the carpeting, although in my experience it was under the baseboard and under the carpeting right next to it.

Good luck.

Quite safe. Just spray the poison at low levels. It won't kill you if you think the pollution around you.
Alternatives: Step on the ants and pick up the cockroach and flush it away!