Going to apply both L2 and EAD, Can I do it together to save time?


Both me and my wife has been on L1B visa (valid till July'15) with companyA for past 3 years. After recent changes in company, I wish to leave CompanyA and join CompanyB. 

Hence I want to apply for L2 visa and EAD. In this process, I have few questions. If you can help answer them, it would be really helpful.

1. To save time, can I apply them together? Meaning fill out I539 and I765 and submit together?

2. Can I e-file these forms or is it better to submit them in paper?

3. Since both me and spouse are already in US, does my application need I129? Or Is I797 (of CompanyA) enough along with I94 and passport copies?

4. Do I need to resign from companyA before applying for L2/EAD or Can I specify a tentative separation date in forms?

5. Do I need to return to home country for any of this process? 

6. If I stay in US during COS, how can I obtain L2 visa stamping? Is there any timeline restriction to do so?

Thanks a ton for your help. I really appreciate it.