I am applying for k-1 visa for my fiancé. Since he usually receive his mail from his mailing address, that's his work office.

If your mailing and physical address are not the same, then will have to list each.

You clock will have reset if by the time you start your new H-1B tour you will have remained outside the US for at least one whole year.

What are my odds of getting a j2 visa?

Married or not, you will in all likelihood still be confronted with the same inadmissibility grounds that led to your visa being denied 3 times...

Can I work for a US company outside the US with a green card?

I agree with Mr. Behar's excellent detailed answer to your question.

Received RFE for I485, to send proof of spouse US citizenship?

Do both with a detailed letter and don't forget to attach a legible copy/proof of your having applied for N-400.

Can we work with valid EAD which expires on June 02, 2020 with pending I539 ( Extend I 94) in process?

No. Cannot continue to use your EAD if your I-94 expires.

Lost visa and Ds 2019?

I agree. Work with an experienced lawyer in this situation.

I am planning a vacation on to Puerto Rico from Boston. I am not a United state citizen or permanent resident. ?

No problem. Travel to PR is considered domestic travel.

J1 to F1 visa?

Of absolutely of no consequence to your eligibility for F-1 visa at the consulate.

I have a RFE for my current H1B petition, RFE reason is LCA :

Your employer needs to engage a competent and experienced attorney to deal with this.