Home Depot...1 gallon size for hops, 5 gallon size for a small BIAB set up. https://www.homedepot.com/p/HDX-5-gal-Elastic-Top-Strainers-2-Pack-11573-36WF/202061360
You can get a fancy, expensive version but I've gotten good mileage from these. I have a bigger pot now and can't use the 5-gallon size for grain, but the gallon-size for hop bags are great.
yep...
I don't think you'd have to worry about cooking the bag inside the boil pot unless you were really wailing with a big burner. Anything sticking out of the top, though will melt if you've got high heat. I use a spring clamp notched into the handle of the pot so that the bag end is up and away from any heat. Also, I have electric now so I don't have to worry about melting bags.
This is how I suspend my paint strainer (hop) bag in my kettle. Works like a charm, I find that I have to squeeze the bag pretty good after the boil. That is 1/4" stainless steel tube that I took from the scrap bin at work.