AOS application for 1st wife is not permitted. Maybe able to sponsor biological kids from ex-spouse. Consult with an experienced immigration...

One week wait appears to be too soon because of immigrant intent issue. 180 days is best.

Assuming your computation of days are valid, it appears you may not have problems with continuous residency during the statutory period. Good luck...

In general, USCIS may. It depends on the nature of psychological consultation. If requesting a waiver for 312 disability exemption, Form N648 is...

There is no harm in filing a nunc pro tunc while in proceedings, for the IJ to consider.

Yes, an I751 may be refiled while in removal proceedings.

Yes, you need an ADIT stamp and receipt for I190 to travel. Good luck.

You may apply for a tourist visa while the I130 is pending.

For the I130 petition only taxes may not be required, but will be necessary to file for AOS. Speak to your lawyer for best options. Good luck.

Probably yes. Speak to an immigration attorney to review your immigration history.