Help understanding relativity?

One thing that’s really puzzling me is how when traveling close to the speed of light when time almost stops for you and everything on the space ship slows down, still the ship doesn’t slow down.
To me on the ship would it seem to me like I’m traveling faster than C?

Also if I travel close to C and turn on a touch the light would travel away from me at C.
So if an observer watched me traveling close to C and turn on a touch would he see light traveling C + my speed?