During REM sleep, when active dreaming is involved, it is not unusual to perceive that you are being touched.
It means that you are dreaming that you are hearing someone call your name ot that someone is trying to wake you. Because as you say in your question, YOU are asleep.
The dog is dreaming and chasing something so they run.
To be asleep, or to be dreaming.
No.
because your asleep, your brain is not functioning well, or you could be dreaming a good dream
When you imagine/plan how your wishes/goals will come true and you are not asleep.
Of course it's normal. Everyone thinks about something or someone before falling asleep, it would be impossible not to do so.
he's dreaming about his angel.
Fall back asleep thinking about that dream.
It depends on what you mean by aware. If you mean aware of the world around them, yes it, happens all the time, your senses, especially hearing, do not shut off when you fall asleep, but most of the time, what you hear will be incorporated into your dream. If you mean aware that they are dreaming, or able to affect things in their dream, again, it is possible, Its called lucid dreaming.
Yes, they are different states of conciousness. Basic 'dreaming' usually takes place when one is asleep
When you go to sleep and you dream your eyes move in a rapid movement, referred to as REM or Rapid Eye Movement sleep. That is how you tell when someone is dreaming.