Page splits may cause logical fragmentation (or may not, depending which pages split).

Memory\Page reads/sec (the perfmon counter) is pages (windows memory pages) read into memory from disk because they're referenced in virtual memory but not present in physical memory, ie hard page faults, and isn't even a SQL specific counter. Probably SQL is either being swapped to the page file because there's other stuff on the server using memory or something else on the server is being swapped to the page file