Can I move to the States immediately after filing for political asylum on GUAM?

It is possible, if you file a bona fide asylum claim. You would not be able to change status to student under the circumstances described.

What can I do? Can I apply to a green card and AOS?

Yes, this is possible. You should be careful if you were only recently admitted to the US as a student.

Can I refile my husband petition even though we dont know if we are approved last petition or Deny.

There is no reason to refile the case. Rather, you should be following-up with the USCIS regarding the status of the case.

I-130 and AOS for parent

The USCIS officer will ask questions regarding your relationship for the I-130 and your parent's admissibility for the I-485, such as whether they...

One of the town I live is incorporated and they don't do police clearance certificate? What can I do in this case?

If you can obtain a municipal clearance, try the County Sheriff and/or the State DOJ.

Can I go to Canada for four days and enter US again with my F1 visa?

No. if you depart without advance parole you will have abandoned your adjustment of status application AND may be refused readmission as a...

If your intention is to work for the H-1B employer, why would you need an EAD? Conversely, if you want an open-market work permit, why seek an H-1B?

Perhaps the machine could not read your fingerprint. In any event, the work permit is valid.

Is it possible for me to migrate with him when his wife file a petition for him?

No. Your father would have to file a petition for you after he immigrates.

Can I do CPT from Day 1 of my Masters Program as per USCIS/DHS rules ?

No, this is probably never going to happen. Check with the DSO at your school for further guidance.