I see that you use clipless pedals, and that you do some rides with steep hills. How do you make sure to unclip in time and keep from falling over if your bike runs out of gears and stalls out on a steep climb? I would like to try clipless pedals, but this part makes me nervous.I am going to answer this question literally - as in how do I handle this situation. It may not be the most elegant or standard way to do it, but it works for me.
If I'm in my lowest gear already and a hill is so steep that I sense I am coming to a complete stop, I make one last effort to push on the pedals with all my force and heave the bike forward. This buys me the extra bit of momentum I need to unclip and put my foot down calmly.
But in general, with clipless pedals the key is not to panic. Once you get used to the system, unclipping should be instantaneous. So even if your bike comes to a complete stop and starts falling over to one side, there is still time to unclip - as long as you don't panic and "forget" how to do it.
And on a separate note: If you frequently find yourself running out of gears uphill to the point of stalling out and having to walk, consider that your bike may have the wrong gearing for your style of riding or ability. Talk to your local bike shop about lowering your gearing; most likely it will mean swapping out the rear cassette and will not be too expensive. Being able to ride all the way up a hill beats having to stop - whether you ride with clipless pedals or not.