Best to work with an attorney for guidance with cover letter.

Yes your brother may apply for a tourist visa on his own.

Yes you should bring your jointly filed tax returns if marriage based filing.

Yes the doctor should use the waiver form and provide basis for your request. Consult with an attorney for guidance.

You should apply for a travel permit to allow for travel of more than 6 months.

Yes your USC daughter may petition for you.

Yes this is normal processing based on information provided.

Contact the asylum office for guidance of status.

It likely was transferred to process the case more efficiently.

Yes you should receive receipt notices shortly after filing.