We are on H (H-1B and H-4). For I-94, Arrival-Departure Record, can a printout from the web sufficient? We have US driver's licence, which we carry all the time. Do we need to carry original I-797A all the time?
You must carry the I-94 printout at all times. A photo ID is also important. The evidence of status COULD be in the forms of copies, I think. It is not required, but I recommend you do carry it.
For more on this issue watch this video.