What is the best way for my fiancee to apply for visa?

Don't be surprised if any delay in your case is due to your country of birth. Pay attention to current events as it's likely that a travel ban is...

Status

H-4. To get your H-1 status you will need to file a change of status to H-1 which will require a new petition.

What do we do now?

As long as it is a bona fide marriage, there is no issue with the age difference. It may be scrutinized more than a regular case, but if approached...

Get a divorce months after filing form I-751 but before the Petition is approved.

You should be fine. Be sure to have records of the divorce and any additional proof of good faith marriage on hand if requested by USCIS.

Need to know the next step

Speak to an immigration attorney who can discuss your options with you. Be sure to have the documents related to his ban.

Travel within the U.S. will not be an issue.

You can if you can establish that you did not enter the U.S. with immigrant intent.

Green Card for brother

File through you as it's a start and pretty much a guarantee. That does not preclude him from exploring other options. Speak to an immigration...

My employer says they didn't get a Fedex tracking number

It does sound suspicious that they wouldn't have a FedEx tracking number. Receipt notice should not take a month either. Should have had an...

Do I need to apply for change in H4/EAD during my employer change ?

Her h-4 and EAD are dependent on your status. As long as they are valid for a period that is covered by your current status, there is no need to...