Hypnos

Seems to be 2 issues, lying on the F Application and any potential bans.
 
Credibility on the H1b as you have lied in the past they may wonder what else you are lying about.

Yet. The CO would be the one to determine if there was a material misrepresentation made resulting in the inadmissibility. CBP rarely gets into those details - they generally document things, deny entry, revoke any visa, and let the embassy/consulate deal with it from then on out.

FYI (and to be clear, being inadmissible means you are banned from entry)
in my non legal reading, the false statement you made and signed to on your J visa application meets all of the following ... as I think it was jan22 explained previously 
 
B. Willful Misrepresentation
Inadmissibility based on willful misrepresentation requires a finding that a person willfully misrepresented a material fact. [2] For a person to be inadmissible, the officer must find all of the following elements: 
The person procured, or sought to procure, a benefit under U.S. immigration laws;
The person made a false representation; 
The false representation was willfully made; 
The false representation was material; and
The false representation was made to a U.S. government official, generally an immigration or consular officer. [3] 
If all of the above elements are present, then the person is inadmissible for willful misrepresentation. 
 
https://www.uscis.gov/policy-manual/volume-8-part-j-chapter-2

Good luck. It's going to be needed. There's a very potential material misrepresentation bar, which carries a permanent (waivable) bar on any visa.

You have no greater chance of being accepted for any other non-immigrant visa than a B visa imo. You don't get away with working illegally in the past because you want to work legally now ... which is basically the message you should have taken on board when you were denied entry on your J visa.

The odds of you getting a visa to go back and work at the place where you worked on a couple of trips in violation of your admittance status (visitor) are almost non-existent.  With any vIsa application, the CO will have to determine if you made a material misrepresentation during  a visa interview or at the Port of Entry.  The answer to that is, "Yes, you did" -- most likely at both.  Discussing your plan to work prior to entering the US and then applying to enter as a visitor for pleasure via ESTA is misrepresentation -- especially the second time you did it, since the first time you could claim you were thinking about it, but weren't sure you were really going to.  Clearly, the second time you knew what you were going to do.  Lying about it during your J1 visa application is even more clear as a material misrepresentation, since the visa would almost certainly not been issued if you had told the truth.  There is a lifetime ban on all visa categories for fraud/misrepresentation.  While there is generally a waiver of the ban available -- albeit it a slow process --  most likely it would not be waived until some time has passed after such a recent nisrepresentation.  
 
The whole arrangement for the O2s sounds shaky anyway -- the purpose of an O2 is to support a specific athlete in an event/performance, not to support a director of a program; he cannot assign you to any other athlete to coach -- only him. And, it can't be used to coach a team or conduct a soccer class/seminar.   I, personally, would not put my trust in what anyone says about getting me a proper work visa when I know the person hires undocumented (i.e., no work authorization) workers as he did you on ESTA.  Just my opinion....

Get with the senator for your district in Washington, D.C. They have people that can help. Ours helped us greatly with i90 issues.

Agreed.
Agreed. Yet, one could assert per 8 CFR §21.1(e) that OP didn't violate F-1 status:
F-1 students may accept on-campus employment that meets certain conditions. OP's employment meets those conditions and the current I-20 expires in December.
 
I do concede that the above assertion is an untested legal theory.

EAD is a benefit, not a status in itself. One can hold multiple benefits at a time - some via status, some via permission from DHS.
Performing an activity that violates your status generally terminates your status. Any other benefits you hold (i.e. work authorization via an EAD and/or authorized stay via a pending I-485) would then kick in.

You remain F-1 until you exercise a benefit (typically using AP or an EAD) associated with your I-485.
 
You don't lose F-1 status by simply applying for or even receiving your AP or EAD, you must actually use them. 

Given your history, your chances of receiving any kind of nonimmigrant visa in the next few years are slim to none. 
 
I could see maybe a B-2 5+ years down the line. Maybe. 

Given your history, your chances of receiving any kind of nonimmigrant visa in the next few years are slim to none. 
 
I could see maybe a B-2 5+ years down the line. Maybe. 

I would go through the office of one of your congressional representatives and try to get one of their immigration liaisons to help. 
 
It's beyond bullshit that their screw-up now becomes your problem through absolutely no fault of your own. 

COs tend to take a hard line on people who have violated status in the past; and you exacerbated this issue by then lying about it (you technically perjured yourself by knowingly signing the misrepresentation on your visa application). Stranger things have happened, but I’d expect future non-immigrant visa applications to result in denial.

https://www.uscis.gov/feecalculator

https://www.uscis.gov/feecalculator

Risk? Yes. Technically you lose status automatically by not filing, although it gets more complicated than that so it's only half true. Basically, you are permitted a continuance and to obtain evidence of LPR status until an IJ makes a final decision. A couple months late filing isn't good, but there have been people in worse circumstances that have removed conditions in the end.

That’s correct. True, unrelated orphans do not have this requirement which is how people adopt babies and toddlers from China, for example. That’s why there was an outcry with one of Madonna’s  adoptions - there was concern that the child wasn’t a true orphan. 
 
If one parent is still alive then the residence requirement kicks in.

Yes it's possible to be detained while trying to fly out of the US. However, it is exceedingly rare if the only issue is an overstay....they essentially want you out.
Note that you won't go through any sort of immigration counters on the way out. The US doesn't do exit controls that way.

It was automatically revoked on day 1 of his latest (and final ) overstay.

No reason is necessary. 

Whether the new husband is a USC or a LPR wouldn't matter in regards to her naturalization--from what I understood in the original post, she obtained the 10-year green card in 2014...she remarried in 2019.
 
 
 

DO NOT engage in any sort of marriage ceremony/celebration/whatever before entry into the US on the K-1 visa. The visa may be denied as a result, or you may be denied entry into the US, even if not legally recognized. If it is a legal marriage in any way under customary or statutory laws, it can be considered fraud to obtain or use a K-1 visa.
Just to clarify, a requirement of the K-1 visa is to marry within the US within 90 days from entry.

They don’t need to be notarized. They don’t even need to be translated by a professional. I translated my own. 

Getting somewhat ahead of yourself, meet first.