Can i extend the 1-751 (remove conditions on residency) application time past the visa date stamp on my passport?

They will change your appointment request once per your request.

I want to apply my grandmother & aunt to come to US on a B-2? visa for non-immigrant visit. Which way is faster?

There is no quickest method. Follow the instructions on the Us Embassy website for applying for a tourist visa.

Completing current class while waiting for COS approval

Yes so long as you show the receipt of the change of status request to your school.

I am amercian and my fiance that lives in turkey on a student visa . He is iraqi, we have been together for 4 years never met.

If you apply for a fiance for him you must prove you met in person unless it is against your cultural norms or causes an extreme hardship.

Yes you can visit your native country.

If they received I-130 in May should I be expecting an answer in September? (hopefully)

It depends on what kind of answer you are looking for.

Eligibility to file if not met the continous residence requirement.

They should be fine so long as they have been in the United States for 30 months.

Hi, I'm from "A" country and live in another "B" country. I'm visitin my home country "A" and have a chance to get police

Yes, you police clearance should be fine.

Hello. I am applying for US Visa, B1 category from China. What should I write in home address and mailing address in the DS160?

Write where you live and normally receive mail.

Asylum case address change before fingerprinting

A change of address does not stop the asylum clock.