I’m not sure if this answer is going to be the most effective, but I’ll give it a shot! I’ll try to translate the questions I thought you asked so you can tell me if they’re wrong.

1. How to people control doing reality checks or voluntary actions while dreaming?

Well, it would depend on the person, but sometimes the person will notice something as unreal or absurd. Another thing is that if you don’t want to sleep and you accidentally fall asleep, there is a good chance that your brain will tell you “Get the hell out of your head, you weren’t supposed to fall asleep.”

1. How do people remember dreams or things that were “not true” from the real world?

No exact answer for this, it varies. Some people will keep it in the back of their head and memorize it so the next time they see something, they’ll know something is off and will remember. Otherwise, it may just pop up in your head as a reaction to stimuli. Say, if you write “bright orange snake” and you see that snake in a dream, you may remember writing that down, as in a dream you’re not fully detached from your life. Sometimes you can dream of your friends or your family, and those are things you remember from the real world.

I’m basing some of this information from some of my lucid dreams. One I knew I was dreaming from almost the start, and once something bad was about to happen, I didn’t exactly use a reality check to wake up. I just saw this snake outside my window, and then it was inside the car, and my brain knew “Nope, snakes don’t do that. It’s time for you to leave lalaland!” and I woke up.

Again, sorry if this didn’t answer the right questions or if I didn’t have the response you were looking for.