Yes, getting married would certainly help him. After marraige you may file petitions for him to adjust his status. You mention he is on TPS but...

Can I travel to Puerto Rico to help afflicted people?

Yes, Puerto Rico is American land and needs no visa to re-enter the USA. Goodluck Ekaette Lawyers.

How can i acquire visit visa after being rejected on basis of 214(b), i have to give my USMLE step2 CS exam?

If your intent is to travel to take USMLE examination then it avers to your intent to immigrate to the USA at some point in the future. As such...

Do I fulfill the continuous residence requirement for citizenship?

You may benefit from 'A Guide to Naturalization' which can be found on uscis.gov. Goodluck. Ekaette Lawyers.

You may not obtain a COS without being in lawful status/maintaining lawful status. A pending asylum application is not maintaining lawful...

Immigration to the usa ?

A k-1 fianve visa would appear appropriate in your situation. Please review my previous answer to your question. Goodluck Ekaette Lawyers.

It appears you have a lawyer suitably positioned to attend to your immigration needs, utilize the lawyer. Goodluck Ekaette Lawyers.

Form I-131 Re-entry form?

The form I-912 fee waiver form is unrelated to the purpose of your travel, rather your income level and your inablility to meet the payment. Form...

Immigration from Manaus,Brazil to USA?

A K-1 visa appears a viable option, it does however invlolve your meeting each other or a reason why such a meeting cannot take place prior to...

If you file I-485, and it got rejected because you were out of status, can you still apply for green card?

You need to be in valid status to benefit from employment based AOS up to the time of approval of aforementioned AOS...