EB2 NIW I-140 Approved

Hello ,
My EB2 I140 NIW was recently approved.
As per my understanding my spouse is now eligible to apply for H4 EAD .
Do we need to apply for that ourself ? Does she need to stay in US while approval is pending ?
Since I have NIW does that help me with my priority date to move fast track in any way ?
When I do international travel and come back do I need to show my i140 ? or just i797 and visa stamp is enough ?

You can apply H4 EAD yourself or hire an attorney to do it for you.

At the time of entry to US, they can ask for any document that they want. So, its better to have some kind of copy with you.

Travel While H4 EAD is Pending is allowed. Pending H4 extension or COS may be abandoned, H4 EAD may receive RFE to prove H4 status by sending new i94. Travel While H4 EAD Pending (H4 Ext, COS Abandon, New Stamp) - USA