I don't like blowing up a task with loads of unrelated additional wishes after the original request was fulfilled. At most the first request can be considered part of the original request. The other requests should be handled in multiple separate tasks.

Optimization requests:

The check happens whenever the user selects or deselects one (or more) certificates. All actions that require conditions not met by the selected certificates are disabled. Some conditions are too complex/slow/special to check, e.g. the check if an empty smart card is inserted should happen when the user triggered the action.

The action shouldn't be enabled for keys not meeting the requirements.

This sounds good.
Will this checks be done on opening the context menu for a private key?

Regarding the requirements for a key: The action shouldn't be enabled for keys not meeting the requirements. (Just like most other actions are only enabled for a suitable selection of keys.) The info which keys are suitable belongs into the manual and not as wall of text into Kleopatra.

You forget that multiple OpenPGP smart cards might be plugged in. Although it's probably not likely that multiple empty cards are plugged in. (For comparison: The subkey action to move a key to a card allows the user to choose a suitable slot. I think it also offers non-empty slots, but I agree that for the "simple copy" it's better to offer only empty cards to prevent a disaster.)