#1 he do not need to wait for COS approval. He can go anytime assuming consulate are open and allowing h4 appointments. Just be cautious about travelling these days.
#2 He wont have any status but he will be in period of authorized stay until H1 to H4 COS gets approved or until he gets h4 stamping whatever occurs first.
#3. He can apply but it wont called H1 tansfer because he is not in h1 status or h4 status. he is in period of authorized stay so for new H1 petition to approve first H1b to H4 COS status must get approved. you should consult attorney regarding same.