Hi there. My trianer told me to use a release word that we don't use every day. She's seen cases where a dog is put into a sit/stay (for example) while the owner chats with a friend. While chatting, the owner inadvertently uses the release work (like "okay") and the dog thinks he's been released. So she told us to use things like "ketchup" or "giggle". Something in a language that you don't speak often works really well. It's really just supposed to be a sound that's associated with the release action.
To answer your other question, yes, every time they move before being released, you have to put them back into position and then release them. To minimize the "stooping & standing" thing, you can use their leash to help you. For example, when teaching "down", you stand on their leash with one foot while holding the end in your hand. Give the "down" command, and if they don't comply, you gently pull on the leash so that it's sliding under your foot, and their collar is being brought down to your foot's level. A little pressure should give them the idea and they should go down on their own after that.
Mind you, if they're not at the level where they're responding to verbal commands/hand signals (ie. you're still having to physically put them in a "sit"), maybe you should be stepping back in their training and put off the "stay/release word" training for now.
Hope this helps!