"What unseen forces allow a rider to balance while pedalling? Why must one initially steer right in order to lean and turn left? And how does a bike stabilize itself when propelled without a rider?"
Watch an interesting video which demonstrates how we turn by leaning in the opposite direction before the turn, or for a more academic study, you can also read this article in Nature.
We do this intuitively so don't worry about it, just ride!
Many cyclists use standing -- pedaling up out of the saddle -- only for hard efforts such as sprinting or steep grades. It's stand, thrash, sit. Learning to stand while relaxed is a great addition to a rider's skillset. It engages different muscles than pedaling seated, making it a nice way to give those seated muscles a rest or a stretch. It's useful on long climbs. Being comfortable transitioning smoothly between sitting and standing is also helpful on rolling terrain or on rough ground where maintaining momentum is important.
For anyone who isn't confident about cornering...
On a group ride last year I saw a rider misjudge the Larimie-Hardie corner on the descent and end up far into the opposite lane. Fortunately there was no oncoming traffic. The next time could be much worse. Given that hills and curves are part of what we love about riding here, how can we corner more safely and confidently?
Let's look at a few common problems: