How can I find out if I received a bar?

The first question, before determining whether you are subject to any reentry bars, would be to determine which visa you may qualify for. As to the...

Probably the information online has not been updated. You could schedule an infopass if you want to check.

If the application for changing status from B2 to F1 is denied, how the unlawful stay would be counted?

You would be in unlawful status when th I-94 expires.

Few weeks ago got a email off uscis saying they are moving my case to another office

The expressed idea is to speed things up. Hopefully it will happen since there is not much you can do about it.

There is no way to expedite the process. You simply have to wait for your Priority Date to become current.

What time is considered to obtain US citizenship?

Your two years as a conditional resident will count towards eligibility for citizenship.

Is What I Did Considered Illegal To Pursue A CR-1 Visa?

I don't believe you will have a problem as you did not try to adjust but rather left before the expiration of your I-94.

How to obtain citizenship for a displaced person brought to America by US Military as a child who fell through the cracks?

He needs to see an immigration attorney. As mentioned by my colleague, relief under VAWA may be a possibility.

Travel back to US on H4 while husband H1B amendment in progress

You should always answer with the truth.

You may be eligible for a U visa. Consult an immigration attorney.