Currently I am in 1st Semester in my Masters in CS . I would like to call my spouse on F2.

The best time is when you are ready. No way to tell what if anything will affect your F-2 from the tourist visa denial from what you said but note...

Where Idaho State asylum interview office located?

The asylum office is located in Chicago, Illinois

Can I get a temporary working visa or social number as tourist?

You are not allowed to work with just a tourist visa.

Handling green card approval while outside USA

You cannot travel on a GC or AP you do not have. Yes once you get them from your wife you can use them.

One for petitioner and two each for beneficiary

Can I use I140 with former employer to file I485? I left the company 4 months after the approval, I485 wasn't filed then

If approved for adjustment you can return to the former employer.

Can I change my status to permanent resident through employment by way being grandfathered through 245i eligibility ?

It does not appear that you have a qualified petition that you could act on under 245i.

Would unemployment benefits affect me getting the citizenship in future?

No as it is insurance and not an assistance program.

Overstayed Visa - Flying Domestic Chicago > Dallas

ID confirmation is the concern on domestic flights. Be aware that border patrol has a presence in both airports.

PR applicants living in US, can they get docs to work while application in process?

Authorization to work is available once the adjustment documents are filed. Traveling a problematic on F-1 once I130 filed.