Dear experts,
Please help me to clarity these queries.

My wife stays in US with H4 visa (non EAD). She got a sponsor to apply H1B visa for 2017-18. H4 visa is valid until 2019.
Assumption: She got the lottery and her petition got approved.

My questions :

1) Can she travel to India now? She has to go India in mid of March'17 and planning to come back in Aug'17 .
2) Does she need to go for H1 visa stamping in India?
a) If answer is NO to above question - While returning can she enter into US with H4 visa as her H1B is still not active until October'17?
b) If answer is YES to above question - by any chance if her H1 visa got rejected or RFE can she travel back to US with H4 visa?

3) Assume, she came back to US with H4 visa, will she be able to work on H1 from Oct'17 with H4toH1 conversion (without H1 stamping on her passport)?