This is correct, although with the newest Henkaku you no longer need to activate it each time you turn it on.Yes.
If you are on 3.60 firmware then you can run the HENkaku exploit through your Vita's browser by just going to henkaku.xyz. It will allow you to run homebrew for the time you have your Vita on. If you restart your Vita it will go away but you can redownload it through the website on your Vita again. If you are on 3.60 firmware DO NOT UPDATE IT unless you want the HENkaku exploit to not work.
If you are not on 3.60 firmware there isn't anything to my knowledge related to mods, hacks or homebrew. HENkaku, the only known exploit at this given moment only works on 3.60 firmware. Not on any firmware below, or above.