Don't worry...you sound like you're doing a lot better than I am and this is my 4th year riding with nearly 10K miles under my belt!
Starting...I used to start like you with your butt on the saddle. Then I learned to clip in with my right foot and push myself along with my left foot until I get enough speed to get my butt in the saddle and my left foot on the pedal. I cannot clip in at 10:00 or 12:00 and then push off with a big pedal stroke...it feels wobbly and it freaks me out. Unfortunately my method of starting means I absolutely cannot start on an uphill, which is limiting. I know exactly what you mean about seeing how other cyclists look strong when they start. I want that too!!!
Standing up...I cannot stand up and pedal. I have tried it but it feels so unbalanced and scary...I have a total complex about it now. But I ride very hilly terrain and I can get up steep hills ok without standing. So if you don't feel comfortable trying it, use your granny gear and keep your butt on the seat like me!
Stopping...Sounds like you've got the hang of this, which is great! I think this is probably the most important from a safety standpoint. You have to be able to stop safely. Unfortunately for me, I am a moron when it comes to stopping and I avoid it whenever possible (even at stop signs!!!). I unclip both feet and wait for the bike to tip until my foot hits the ground. Can't do the one-foot-clipped-stand-on-the-pedal thing. Tried it, tipped over twice. Now I have a complex about that too.
There is good advice from other posts here and I bet you will do fine. Even if it takes you a while, just remember you're doing better than I am!!!!

