APC Object Cache provides a persistent memory-based backend for the WordPress object cache. APC must be available on your PHP install.
Yes! APC 3.1.1+ supports incrementers and handles its own cleanup of expired objects, so it works just fine for Batcache. Lower versions of APC will work, but the hits trigger will be disabled.
Maybe, but I'm not going to support them, and you shouldn't still be running them!
WP_APC_KEY_SALT to something that is unique for each install (like an md5 of the MySQL host, database, and table prefix).