Both can relate to ground, but they are not always the same.
With falling, caer al suelo is a very common expression. It sounds natural and idiomatic.
If you said cayó a la tierra, it would sound more literary, poetic, or like you specifically mean the earth/soil.
Both cayó and se cayó are possible, but they can feel slightly different.
With people, se cayó is very common:
With objects, both are used, but cayó is perfectly fine here and sounds straightforward.
La hoja se cayó al suelo is also possible, though cayó may sound a bit cleaner in this sentence.
Yes, Spanish word order is somewhat flexible.
The original order is natural:
You could also say:
That puts more emphasis on the cause.
You might also hear:
So the given order is a normal, clear way to say it.
The accent marks show which syllable is stressed.
Without the accents, the stress would be read differently according to standard Spanish spelling rules.
So the accents are important for both pronunciation and correct spelling.
Most likely, yes.
The definite articles suggest something specific:
In context, this usually means a particular leaf from a particular tree, and the wind as the relevant cause in that situation.
Spanish often uses the definite article where English might also use the, but sometimes Spanish uses it even where English would be less explicit.