I don’t believe the Cardinal has a public email address published let alone a private one. Typically your best bet is to call the main number and ask to speak to a secretary in the Chancery or the Cardinals secretary. Ask her what the best way to send a message to the Cardinal is.
I imagine every bishop is different but in my diocese they request a written letter, which is reviewed by the bishop and then directed to an appropriate person for a response. Bishop does actually see them every letter addressed to him, though the response rarely comes from him.