Driving license when in the process of moving from H1B to H4

[divya.trivedi]

I was on H1B till 11 June of this year. My employment ended on 11 June and I am now in process of getting converted to H4 (spouse is on H1b). i.e. spouse's company is filing form I-539 for me.

What is my status currently?

Do i need to do anything else? i.e. inform USCIS myself too? Should i do anything wrt COS?

Also, I want to get my driving license. Will NJ DMV allow me to give written/driving test?

Thanks in advance