What do I need to enclose to get this situation resolved?

I agree with my colleagues. This is not an immigration question.

I agree with my colleagues. Contact your DSO prior to leaving the US for a final review.

Is there any other way to adjust her status. I did not understand the last part when they say other avenue exist. What avenues.

I agree with my colleague. Contact a US immigration attorney to review the denial in detail and determine your options based on your current green...

Will I loose my OPT if I utilize CPT for more than a year continuously?

Contact your DSO and/or school's US immigration attorney to review your situation and determine future OPT eligibility.

F1 reinstatement and TPS at the same time?

I agree with my colleagues. Contact a US immigration attorney for assistance with your TPS filing.

I agree with my colleagues. Contact your DSO and/or US immigration attorney for review.

1. Will I be prohibited from entering the United States if I leave? 2. May I file another I-485?

I agree with my colleague. Contact a US immigration attorney for a review and prior to any departure from the US.

Is it possible for me to a) obtain a visa for a third country such as UK while in the US and b) get my renewed H1B visa stamped

I agree with my colleague. Contact your company's US immigration attorney before leaving the US.

Can I travel out of the country and return with old visa and renewed H1B petition?

I agree with my colleagues. Contact your company's US immigration attorney for assistance prior to leaving the US.

Am I safe to travel when my name on my green card is missing my middle as it's shown on my passport?

I agree with my colleagues. You should be able to travel freely as long as the green card and passport are valid.