I very rarely ever use cruise control, but I used it a few times on a recent road trip. From what I can remember, and from my recent experience, I've never had either of these two things happen. Pushing on the accelerator while in cruise control mode should make the vehicle speed up until you let off, at which time it should coast back to the original set speed. When you need a little extra power to maintain the set speed, it will downshift just long enough to get you back to that speed, then resume the original gear. This is how mine has always worked, so I suspect there may be a problem with yours if it behaves the way you described.
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