How do they feel?

Well, basically, it's like this:

If I were to tell you, RIGHT NOW, that you were dreaming - and I proved it by levitating off of the floor - how would you feel?

That's how it feels.

It varies, depending on your present state. If you were groggy and you'd just woken up - it would feel one way. If you'd just got done running a 100-meter dash and you were full of adrenaline, it would feel another way. Basically, it's just the realization that you are dreaming. So there is no "set feeling" for it.

And yes, you can "die" in lucid dreams - but what happens after you "die" is different. And, even whether or not you "die" is not set in stone. Allowing people to shoot me, at point blank range, is actually one of my favorite things to do while lucid. The look on their faces is usually priceless. Lol.