Less risk than not telling the truth
2) I just applied for AP but not sure if I can get it by the time of travel. Suppose I have AP when I travel and I still apply for H1B visa stamp. If I get the H1B visa stamp, then I don't need to use AP. But how about if the H1B visa is rejected, can I re-enter the US using AP in this case?
You can use H-1B visa or AP (even H-1B disapproved)
3) In case I use AP, I don't have to have valid EAD card, do I? (I used my OPT-EAD card for half a year before getting H1B).
YES