H1 and H4 Extension applied on same date. H1 approved, H4 still pending.

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My H1b Extension got approved on Dec 5th but when i checked my wife's H4 extension case it says Name was updated on Nov 7th.
1. When it shows 'Name updated on Nov 7th', does it mean this case will be processed from initial stage and starting from Nov 7th ?
2. Is it recommended to cross country with out Valid H4?
3. I understand we can change these cases to Premium, can we change H4 case to premium too? If so, how much does it cost?
We are planning Visit India in Jan Last week, would you suggest to wait for USCIS to come back with update or change the process to premium?

Appreciate your response.

Regards.