Renewal of passport for my spouse on H4

[keshav.phoenix]

Hi All,

Can you please advise on my below situation.

I recently changed the job in US from company X to company Y. My H1B was valid till 2018 Dec with company X and after switching the job, I got I797 till Apr 2019. 

My wife recently came to US from India on H4 Visa while I was with company X, so on her current passport H4 visa is valid till 2018 Dec and has company X mentioned on it.  Since I changed the job after her arrival to US, I have requested for amendment in my wife's visa also with my new employer company Y(I guess its called I539 and I have not received any paper regarding that).

Additionally her passport is expiring in next 4 months(Apr 2017), so she got I94 till Apr 2017. Now we want to apply for new passport from USA. We thought it will be safe to have an alternate ID proof(state ID) before sending her passport for renewal. When we approached DMV(Illinois) for state ID, they said they cant issue state ID for a I94 which is expiring in 4 months. 

Now my Questions/Concerns are

1. Will the visa details get updated in new passport? If not what I need to do to get it updated)?

P.S: I'm sending my latest I797 copy along with other documents for passport renewal

2. Is it safe to send her existing passport for renewal, without having alternate ID proof?

3. Does my wife(H4) will also get an I-797? Do I need to pursue for that document in my new company?

4. Do I need to purse for getting I539 in my new company?

Thanks in advance,

Keshav