Only if her visa will expire before she will travel to the US or if it is already expired.
No issues, just sent her the original I797 and have her present that along with copy of primary H1B I797 and other supporting documents to the CBP at port of entry. Make sure she has a valid H4 visa when she travels back.
for Question #3:
I rather meant to ask when her H4 is already expired and If she travels to India (while her H4 extension is in process), since she is planning to stay longer and during her stay if the H4 extension gets approved, can she use the approved H4 extension for stamping ? or is it the process has to be like the one we do for first time stamping ?
She can simply use copy of primary H1B I-797 for stamping (like first time stamping). She don’t need the EOS approval notice for H4. However when she travels back, have her carry the H4 EOS approval notice along with other documents.