What do I need to do to make sure I re-enter US without issues?

You would need to carry your expired green, I-751 filing receipt and your passport.

Traveling with F1 Visa

Not sure what you mean by your adjustment of status? You filed an I-485? Or you mean your change of status to F-1?

Do I need a joint sponsor?

The key is the most recent tax filing plus your current employment.

LPR, filed for wife on B1/B2 visa, I-130 approved, category retrogressed, can file again or revive old I1-30. Im now a citizen.

When was the initial I-130 filed and did you get a copy of the Approval?

Timing question: marriage Before / During / After my future wife applies for EB1-A Extraordinary Ability green card

You may want to consider getting married civilly now so she can list you on any immigrations applications she may be filing. At the very least,...

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How many times per year can you visit the US in a b1/b2 visa? the length of each stay is about 5 days.

It is a discretionary matter with the USCBP officer at the airport. If they decide that you are in the USA for B1/B2 purposes then you can come...

You need to speak to a landlord-tenant attorney.

Didn't live together for a long time after on paper marriage and green card petiton

We would need to analyze the case further but is appears that your marriage is a bona fide one for immigration purposes.

What are my options in order to get the I-140 approval notice, or how can I retain my priority date?

A review of the case/file would be required.

1) Can we pursue the drop box facility? 2) Should they go in person for the interview?

In most cases now an interview is required.