This is speculation, but my answer to:
Does an angel earning wings cause a bell to ring, or vice versa?
Possibly when an angel earns his wings he goes on the list to get wings. No doubt wings are given by seniority on the list. And if people across the world ring bells often enough, it might take just minutes or seconds for enough bells around the world to ring and for him to receive his wings. So maybe God has influenced society to make the average frequency of people ringing bells be the same as the average frequency of angels earning their wings. And in this case God would have made a bell ring where George Bailey could hear it just when Clarence was the next angel on the wings list.
Therefore I would say that in the fictional universe of It's a Wonderful Life God spread the story of bell ringing coinciding with angles getting their wings, and also arranges for the frequency of bell ringing and the frequency of angels being award their wings to be extremely similar or even totally identical, for the purpose of reminding some humans of angels whenever they hear a bell ring.
Every time a human who knows and believes the story of an angel getting his wings when a bell rings hears a bell ring, he will think that another angel just earned his wings and he will be inspired to seek similar success.
In short, in the fictional universe of It's a Wonderful Life, God arranges for a bell to ring to announce every angel receiving his wings, to remind the living of angels and heaven and inspire them. God arranges - probably sending angels to take care of it - for bells to ring every time an angel is awarded his wings. Humans deciding to ring bells for human reasons doesn't cause angels to receive wings they haven't earned, and angels receiving the the wings they earned doesn't cause humans to ring bells for no humans reason, instead God arranges for the two events to coincide.
Note that the saying that whenever a bell rings an angel has received his wings is either made up for It's a Wonderful Life or an old superstition.
According to the theology of most Christian denominations, angels don't earn their wings, and don't even have wings, except when they decide to.
According to Christian theology angels are beings of spirit and as old as Creation or older. Angels don't have physical bodies, but when they interact with the physical world they can make bodies - bodies of any imaginable shape or design - for themselves out of matter. Thus they don't look like humans with feathered wings, except that when interacting with humans who are conditioned by art to expect angels to like that they might - or might not - decide to make bodies that look like stereotypical angels in art.
And the same goes for devils, who are considered fallen angels in Christian theology. Many important devils have highly individual forms they take when interacting with humans.
Asmodeus, for example, is sometimes depicted looking like this:
Since angels are ageless and don't reproduce, there are no angels that need to earn their wings.
Many stories claim that good people become angels when they die, and thus have to earn their wings.
One example is the 1982 TV movie The Kid With the Broken Halo in which the recently deceased Andy LeBeau (Gary Coleman) is an angel in training, trying to earn his wings, and constantly goofing up and getting into trouble. Thus he is given one last chance to prove his worthiness - or else go to the other place.
But angels and the souls of good deceased humans are like two separate species, totally different, with different functions in heaven. Except that describing angels and humans as two different species is understatement.
Members of different families, and orders, and classes, and phylas of biological beings are in many ways much closer to humans than angels are. Plants and bacteria and rocks and computers are related to humans much closer than angels are, and even the most bizarre aliens from outer space are more similar to humans than angels are.
At least according to Christian theology.