(1) ERROR sounds about right.

(2) CRITICAL would be consistent.

(3) Regarding output -- I'd prefix the message with DEBUG/INFO/WARNING/ERROR/CRITICAL; you can use the colors for server log lines as a guide (e.g., criitical should be purple; info can be green, debug can be cyan).

I'm not sure I understand your comment about which ones to print however -- I would have thought we'd be printing everything.

(4) I'd say be explicit, and refer to the fact we're doing a system check; e.g., 
    "System check identified 3 warnings, 5 errors"
    "System check identified no problems."