1. I recommend getting one with an A1, or maybe A2 rating, A1 should be sufficient. I don't know what your issue is, so I can't guarantee that an A1 rated card will solve the issue, but beeping can be due to a slow card response, and A1 rating should ensure a card that responds fast enough. The issue is unlikely to be related to the card write speed, A and C ratings are totally different things, cards without an A rating only guarantee an average speed given that writes are well buffered by the camera, not that they will keep up at all times while writing multiple video streams with buffering provided by the card. It can clearly work without an A rated card, but not all cards have the same performance even if they appear identical, the A rating does provide more certainty.
2. The hardwire kit should be OK, but it is worth a check with the supplied power adaptor, just to rule out the hardwire kit being the problem.
3. Haven't seen many reports of this since 2.0 came out, not sure if that is because the problem has been solved, or because people are waiting quietly for a fix. From the posts above I suspect most people are now OK? In which case it is more likely related to your memory card...