Expansion is a local property. A loose analogy you might be able to visualize is to imagine standing on an immense sheet of rubber, to which you've attached a bunch of stickers. If the sheet of rubber started to distort so as to make your stickers move apart, you could say that the sheet of rubber is expanding here
where you're standing, even though you know nothing about what is happening everywhere else.
The word "purpose" has connotations irrelevant to physical law....
The notion of cardinality studied in set theory is mostly unrelated to the number [itex]+\infty[/itex] that appears in continuous mathematics.
To the best of my knowledge, this idea is still speculative
-- there is not yet anything to back up the idea that there is a minimum distance, simply evidence suggesting we look for new theories having this property.