I didn't realize that you could roll over HSA balances. In my case it's moot, because the health plan I have doesn't qualify for an HSA, but it's still good to know, if something might happen to change down the road.
Regarding the other stuff, the restrictions on IRAs or our 403b make me uncomfortable, and their tax advantages depend on assumptions about future tax brackets that I'm not all that confident are valid. So we have more than half of our retirement savings in normal investment accounts that are partially taxed as they grow. I'd rather get some of the tax out of the way now than have to pay it all later.
Yes, the money in an HSA is yours and is there forever until you use it unlike an FSA. You can also use it to pay medical expenses even if you don't have a qualifying plan anymore. The money just have to be put in while you have one. Most of the HSA accounts also let you invest the money once your balance is over X. I believe it's $2100 for the one I'm currently on. It's not a full on investment account but more like my 401k where I have a list of funds that I can invest in.
Thanks for the suggesting @Ouchie-Z-Clown on them. I hadn't been thinking of it for retirement and was mainly using it just for my max yearly out of pocket amount. It makes a lot of sense though to put more money in since it's pre-tax money and grow it for my medical expenses when I get old.