Do I have to go through the CAP again?

You appear to be in limbo without an approved H-1B. It would appear that you are not cap exempt, as you currently have no approved petition.

H1b to B2 change of status fro 2 months delay in leaving the country after I94 expires.

There is a new 60 day grace period for H-1Bs which may be applicable in this situation.

Can I choose to not go onto H1B even if my application is picked in the lottery?

That's between you and your employer. Why are they sponsoring you for an H-1B if you already have a visa? It might be easier just to transfer...

Can I still go to Libya and come back to the USA?

Theoretically the new ban does not apply to green card holders. In reality you are likely to see enhanced scrutiny. In the end, everything should...

I 140 job portability with time gap in Employment.

The question is a little confusing. Are you eligible to receive a green card now? I would need a little more information to provide a useful...

While a pending I-485 based on marriage (I-130) , I can go out of United States because of an emergency situation

I would try to file for advanced parole. If you leave now, your green card application may be considered abandoned.

Question 19, part 4. If i am here with J1 visa, is it considered as i've been employed by my host? should i choose yes or no?

Generally, if you are employed and receiving a paycheck then say you've been employed. You can always write a paragraph to explain your situation...

Yes, if it is discovered they lied to the USCIS they can lose their visa and be deported. It affects the person's fitness and good moral...

When can I file for citizenship and when to file for my husband?

Since you a green card holder your can file for your husband's green card now. You are also eligible to file for citizenship 3 months before the...

You certainly can ask for expedited process on humanitarian grounds. Sorry for your situation.