F1 is nonimmigrant student category and has no status to petition for anyone. for LPR. F4 is a 4th preference category of a sibling of US citizen....

The number of children is not a restriction to K1 visa.

Yes, flights interstate with passport is permitted.

You may check processing times on USCIS website.

The I130 may be filled while parents are here on B2. This just establishes relationship not benefit.

With a pending H-4 and H-4 EAD extensions, short term disability claims and medical leave are permitted.

More information and background are needed on the application. In other words, what has been the nature of your inquiry on status and USCIS response.

Yes, US entry for visiting possible, if parent is not involved in the SIJ application. All delays in secondary etc. are foreseeable.

Yes, if no issues or restraint with the court and other criminal justice officials.

With a valid and appropriate US visa, the choice of international airport/port of entry for US entry is up to him.