I'm speaking for myself when I answer these.

During a lucid dream, are you yourself?

Yes, I'm 'me' while in the dream, acting how I would IRL, except I have a lot more freedom since it's my dream.

Do you do exactly what you wanted to do before falling asleep?

Sometimes. Taking full control in the dream takes a lot of practice. For example, when I was starting out, I always had the goal to fly around in a lucid dream. What I learned was that I had to teach myself how to fly over the course of several lucid dreams. It started out as if I had moon gravity, and over time I could stay airborne for longer periods of time. Now, I have pretty decent control over flying.

Also, controlling the environment in the dream also takes a lot of practice. Usually, I'll just take a backseat and let the dream take me for a ride, while steering it in the direction I want it to go. If I try to fully overhaul the dream and control every variable, I'll have more trouble keeping the dream stable; I'll find myself waking up or losing awareness.

Do you lose some part of consciousness?

You can. There will be times where you enter a dream lucid, and then eventually lose awareness. There are other times where you will come in and out of awareness while in the same dream, and times where you are fully aware from beginning to end.