Form I-765

Can I travel while my H-4 EAD is pending?

First of all thank you for all your blogs and videos on immigration. They are very informative and knowledgeable. I follow your views and suggestions on all my immigration work. I also recommend your suggestions to lot of my friends and colleagues. I appreciate your help towards the community.
I have a situation:
I am in my 3rd year of my H-1B status, my I-140 is approved and need to file for my spouse H-4EAD on May 26, but she needs to travel to India for family reasons in August this year.
Questions:
1) Will that be a Ok for her to travel to India while her H-4 EAD petition is pending?
2) How long will the petition will take to come to a decision (~estimate)?
3) What happens if her H-4 EAD petition gets approved and she is in India? Does she have to go to the US Embassy again?
4) (Being positive but need to think the other sides of a same coin) what happens if her H-4 EAD petition gets denied? Will she be able to retain her H-4 status? Will she able to enter US without any issues?
5) What would you suggest? Will that be ok for her to visit (or) to wait till the decision is made on her H-4 EAD petition?

See clip from Attorney Rajiv S. Khanna's conference call video that addresses this question. 

https://youtu.be/8N82R3qAiJo?t=123

FAQ Transcript:

Unless the context shows otherwise, all answers here were provided by Rajiv and were compiled and reported by our editorial team from comments and blog on immigration.com

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USCIS Started Accepting EAD Applications for Certain H-4 Dependent Spouses

REMINDER: Do NOT submit an application for employment authorization (Form I-765) before May 26, 2015. USCIS will not accept a Form I-765 requesting employment authorization based on your H-4 status until the H-4 rule takes effect on May 26, 2015. If you submit a Form I-765 requesting employment authorization on this basis before May 26, 2015, USCIS will reject and return your application with the filing fee. You would then need to re-submit the application on or after May 26, 2015.

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Deadline May 2, 2014, for Haitian Temporary Protected Status Re-registration

Eligible nationals of Haiti who currently have Temporary Protected Status (TPS) must re-register for TPS by May 2, 2014. Failure to re-register by this deadline may result in the loss of your TPS and your work authorization.

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