L3 switch - All L3 processing offloaded to card? On a Cisco 3560 switch, are all L3 processing offloaded to card instead of normal CPU?

On the 3560 switch, as well as on most modern L3 switches still being sold, L3 is done on ASIC that handles a number of things - including L2 switching, L3 routing, ACLs, QoS and so on. "Normal CPU" is being used for chassis management and interaction with the user/admin.

There's no separate "card" in 1RU/2RU systems usually. On the chassis systems yes, sometimes L3 processing is done on a separate daughterboard on the line cards (in distributed fashion) or in main management module (usually called Supervisor).