Is there any way to apply for permanent residency for parents while I am a permanent resident only and not an US citizen?

No. No exceptions. Only USC's can petition for parents.

Conversion of H4 to H1B

Once H-1B COS petition is approved you can start working. You will seek H-1B visa when you want to travel back to the U.S.

Form AR-11 (Alien's Change of Address Card)

AR-11 is to be filed by all non-citizens within 10 days of move.

I agree with my colleagues.

What kind of visa does my British wife need to live and work in the US?

I agree with my colleagues. You have options. Ideally you would go for the immigrant visa. Even if you apply for K-3, it is up to the Officer to...

Do I need to fill I-539 or can I just go the boarder and enter the US with my B1/B2 visa?

I agree with my colleagues. Either way you chose to approach, you will be required to show the non immigrant intent and the purpose for seeking B-2.

N-400 Naturalization form - I became a US citizen about 15 yrs ago, need info from my adjudicated N-400 filed with USCIS (INS)

I agree with my colleagues. Do a FOIA. There is no filing fees for the application. The fallback is it takes a long time to get your file if you...

Came on H1B in 2001, overstayed. Married to US citizen, working as an independent contractor, paying taxes, Can I file I-485?

It should not hurt to have your case reviewed by an experienced immigration attorney before you file.

Can I study/ get a student visa while my green card is processing

You are seeking an immigrant benefit of residency. If you simultaneously seek a non immigrant visa, it is likely to be denied.

My US citizen daughter married an international student. Can she petition for him to immigrate if he is an F1 student?

I agree with my colleagues, she can petition for him. You may want to discuss other issues with an experienced immigration attorney regarding when...