Yes, I unclip my right foot when I need to stop and put that foot down on the ground, while leaving the left foot clipped in. I only unclip the left foot if I'm getting off the bike completely.

To start out, I always clip in with the left foot and start to pedal with that foot, sit down on the saddle, then clip in right after I'm moving. Being seated makes you more stable while you're clipping in with the second foot.