H-4 dependent visa logistics

[Satyanarayan]

Hi, 

My employer is in the process of applying for my H-1B (not sent to USCIS yet), but they don't file the H4 dependent visa. We also had a life change event in April (expecting the passport for the baby anytime in July).  It will be a great favor if I can get answers/suggestions for the following question: 

1. While my H1-B application is pending, can my wife travel with the baby (we expect to receive the passport by mid-July) with a valid F2 I-20 but with an expired F2-visa on her passport? 

2. If my H-1B is in an approved state, it means that my wife's F2 I-20 will be null and void. Will traveling (my wife and the baby) to India be okay, as in can she get H-4 when I travel to India and bring her along later? 

3. How long usually it takes to get an H4 dependent visa?

4. What is the general fee for an H4 visa service if I hire a counsel, and will it help expedite the process?

5. If I go for H4, and it is “in process” with USCIS, can my wife travel to India without any issue? 
 

PS: I did find on this forum that applying for H4 is an easy process, I just have to submit I-539 form and other required documents along with my H-1B receipt notice.