Is fragmentation at non-leaf levels a problem?
No. Non-leaf index pages are particularly likely to stay in cache. In principle, it might slow down read-ahead a little (upper levels are used to drive this) the first time an index scan with read-ahead occurs, but meh. Some people regard fragmentation at any level a normal thing and not something to worry about if the data is usually already in memory or if the storage subsystem has low latency and good throughput.
Because SQL Server doesn't go out of its way to avoid it. Non-leaf pages can experience page splits too. Padding the index above the leaf (PAD_INDEX) is possible but rarely worthwhile.
The clustered index key(s) and any uniquifier.
This isn't implemented.
I believe it is a count of the number of contiguous areas at that level of the index, yes.