Will president Trump's new EO of 06/22 effect my current H-1B status?

The Executive Order applies to newly issued visas issued outside the United States. So if this your situation you may be subject to its terms.

You clock was stopped because you did not choose the expedited hearing date (earliest date).

This will not affect an asylee currently in the United States.

Asylum clock ?

If you had accepted the expedited hearing your clock would have kept running. But, since you deferred your clock is stopped. Once your individual...

Can Ukrainian nationals with valid B1/B2 visas enter the country now/in August?

In general he should be able to enter. Be careful to abide by the terms of the visitor visa.

How many months will there be between between I130 approval and papers processing at NVC

You will have to follow the instructions as provided by the consulate. If a legal permanent resident (not a citizen) is the petitioner you may be...

Changing the category. This is not an immigration question but rather child custody.

Working under k-1 visa?

No, you will need to scrape up the money and submit the I-485 and I-765 and other documents in order to legally work in the United States.

Yes, the ban will likely be extended regardless of the outcome of the election.

You application would likely be stronger if you got the paperwork done in the United States. If you are adjusting status, just find a doctor near...