How long should a Nano ID be?
Long enough that a repeat stays unlikely for as many as you will make. Set the rate you expect and shorten the ID until the time shown is longer than the system will live; 21 characters is far more than most need.
Nano ID or UUID?
A UUID v4 has 122 random bits in 36 characters; the default Nano ID has 126 in 21, so it is shorter in a URL. A UUID fits a uuid column and the libraries that expect one.
Is the default alphabet safe in URLs and file names?
In a URL, yes: none of its characters needs escaping. In file names on a disk that ignores case, as most Windows and Mac drives do, two IDs that differ only in case would clash, so pick lower case and digits there.