Arazia

You know what really grinds my gears, ppl who come on here asking for advice abt their jacked-up realtionships, then get mad at you for giving advice on the truth... If you didnt wanna hear the truth, then dont post in a forum, Pm someone in private...

Hi. I'm sorry to hear things didn't work out. I don't know the answer to all questions but I am from Illinois too, so here is what I know:
That is correct. As Jim suggested, a quick google search might prove to be helpful. There are many guides online on where to go and get the papers you need and how to go step by step through the whole process. A good idea would also be for you to get a mediator. He/she will guide you through so you can do things faster and fill out the paperwork correctly.
It is very nice of you to help him and not kick him out. Illinois is absolutely a disaster of a state, in my opinion, when it comes to finding jobs. And they say Midwest should be the place for the "working class" lol. Now the job market is "moving" a little bit but on a scale compared to other states, 11.something unemployment rate(countrywide that rate went down a bit) as of last month places Chicago almost to bottom of the list with just 4 other US States. Anyhow, that's not something that important but I salute your sense of responsibility. I'm sure your ex is not happy with the situation either. Good luck to you.
In Illinois, even though you live in the same place, if you have separate rooms and have not had physical relations in 6 or more months, then you can wave the 2 years separation and get divorced. You might want to state irreconcilable differences if you want the divorce to be pronounced within a month or two. Do not file on those grounds unless you want to get a lawyer and wait and wait and wait until you'll actually be divorced. Yes, you do qualify for "no fault" if you live in the same place, separate rooms. It is called separation period since the day he moved out to another room and have not had sexual contact with him. I don't think that you will encounter problems of any kind when you decide to get married with your UK now boyfriend, later fiance.
Good luck

Divorce will not affect his status, other than when he will be eligible for citizenship, as you mentioned.
There a many MANY websites that contain forms and advice on filing without an attorney. Do a Google search for "Illinois divorce forms" or "Illinois divorce law".
A "no fault" divorce in Illinois usually requires a 2 year period of separation. You can ask the judge to reduce the period to 6 months, but I think that's the best you're going to be able to do. If you need to file sooner than that, then you'll need to file based on fault. Adultery, while still technically a misdemeanor in Illinois, is very rarely prosecuted. Prosecutors consider it time consuming, costly, and largely pointless. Fornication is also, technically, a crime in Illinois. If they sought to prosecute for it then Oprah Winfrey would be facing a year in jail. There hasn't been a conviction for adultery in Illinois (that I was able to find) since 1943. A case was brought in Harvey, Illinois, in 1997, but the prosecutor refused to prosecute.
On the other hand, people divorce on the basis of adultery quite often in Illinois. There is no recent case (again, that I could find) where the divorce resulted in criminal prosecution of the accused adulterer.
Yes. No waiver needed if this will be your second K1, and it's been more than 2 years since your first K1 was approved.
Not likely to make any difference with the petition approval. Possible it might come up at the interview, but much less likely at the Embassy in London than with a high fraud consulate. Also possible it could come up at AOS or ROC, but not likely to be a problem.

1. Yes, you're correct.
2. No. My DIY divorce was in Texas.
3. When my ex an I filed, our situation was a little similar to yours. He had a girlfriend and I had begun talking to my current husband but we were only friends. The ex and I still filed a no fault divorce citing irreconcilable differences and, since we were still living together, the lack of marital relations for the 9 or so months prior to filing. We had no problems getting the divorce and to this day are still friends.
4. and 5. Having filed for a CR-1, I'm not entirely certain on the time limits between filing K-1 petitions. I can say to expect it to come up during the initial filing and again at the interview. Expect to be asked questions at the very least. If you're on good terms with your husband, then perhaps you can each write a letter explaining the breakdown of your marriage (no fault, remember). He can use yours when petitioning for citizenship and you can has his available if needed during your new K-1 adventure.

Um wow. well technically you ARE still MARRIED so you cannot file anything for anyone else until your divorce is final... And no mean to pry but why are you two still living together if both if you are cheating? What is the point? And if you are still "living together" and you have three weeks left to do his paperwork, why are you questioning helping him?
My thing is if you wanted nothing to do with him, he'd been moved out. He can get his own job or apt and you bein extra nice and caring wont get him to leave- but that is just my opinion.