How long it take for changing status from B-1 visa to R-1 visa ?

It can take several months due to processing delays.

What are my best options?

You should meet with an immigration attorney to ensure no further mistakes are made ASAP.

What can I do to stop deportation? What are our options? Why is this just now an issue? Is there any hope? We want to marry.

You need to hire an immigration attorney as soon as possible - this forum is just for general questions.

Can I married someone that is not a citizen

Yes you can marry someone who is not a U.S. citizen.

Valid H1-B Visa, never used. Entering US with ESTA, changing status to H1-B with a new H1-B approval notice while in the US.

As the other attorney explained in detail, this cannot be done.

As long as the employer files the labor certification BEFORE the prevailing wage expires (or begins the advertising process), it will not matter if...

What additional documents can be submitted to support this mismatch of dates and establish the actual course completion date?

Is your degree from India by any chance? USCIS has started issuing these denials for degrees from India recently. You should get a letter from...

After 12 months of my full-time CPT, could I work on part-time CPT for balance school year?

Your DSO is the best person to answer these detailed questions for you.

Can she still file a motion even if its after 30 days of the decision? Why the SEVIS record doesnt show their October class.

Why was the decision only now received? Did she move?

Can i travel outside USA or will there be a risk while reentering USA?

There could be a risk but you can mitigate it by working with an attorney before leaving.