Updates come as fast as CCP will allow.
This is supposed to be every 5 seconds, but for some fleet statistics it takes longer because CCP gives old obsolete data.
In general, it takes about:
Only the bare minimum. Almost all data simply passes through the server from either a PELD client, or from ESI, to the FC. It is not stored.
To reiterate, the highly opsec things like PELD combat data, fleet location, fleet ship types, are NOT stored on the server.
What is stored: