Will the block data saved or discarded after synchronization? Does it get removed when uninstalling?
The blocks will be stored on your hard drive in the application data directory. If you uninstall, the block files will be kept. There may be an option in the uninstaller that will remove them, but the wallet.dat file will be kept for certain.

Future versions of the mainline client, Bitcoin-Qt, will handle this storage differently via Simplified Payment Verification.