There is no law prohibiting parents of an SIJ from visiting the U.S. on a tourist visa. Beware of possible charges of alien smuggling.

Highly not recommended. The US consular offices are overwhelmed and it may take a very, very long time to get the passport.

It is permissible. If you miss the oath date, it may not be simple at all to get it rescheduled.

No, USCIS does not close a case if you do not file within a year. But if the visa is at the National Visa Center, and you do not follow up, they...

You might not have any immigration status at all. You may wish to file a FOIA request to see what records USCIS has for you.

There is no good mechanism to cancel the H1b since you are not the one filing it. Perhaps you could leave the country and return on your F1.

Check the processing times at your local USCIS office. Go to uscis.gov.

Try traveling to Mexico, staying there for two weeks, and then enter the U.S.

You should wait to hear from them for further instructions. If you actually submitted a picture album, they don't accept such things.

What do you mean you are applying for the first time? You are not. You should not apply for a new social security card either.