malekkk

Yes that’s exactly what happened to me. I didn’t need a transit visa and it was under 24hours layover where I needed to change airport next door. 
But officer was rude and I even gave her the name of the officer who cleared the way for me which made her colleague wonder and told her:” oh he actually knows his name!” 
But she still acted as if I was the wrong doing here, by coming without a transit visa.
And yes I know it’s not a problem for n400 but just worried about like “hmmm.. this guy is making status is US and now UK! So he’s playing games!” Type of suspicion by IO for n400. You don’t think so? Or it’s irrelevant? (Which I believe it is stupid and non sense if IO would have this type of thinking and reject me based on that) 

If you arrived here on the day of or anytime after your second wedding anniversary you were rightfully issued a 10-year GC at the beginning. If you arrived before your second anniversary you potentially have a problem.  
 
Marriages fall apart all the time. 50% of marriages end in divorce - that was your 50%. You are applying under the 5-year rule so the marriage won’t even be considered. 
 
What happened in the U.K. stays in the U.K. incidentally there are hotels inside the terminals at both Gatwick and Heathrow airports. But they are land-side. There are no air-side transit hotels there. The reason you were put in detention in the U.K. is that you were considered a flight risk. Had they put you in a hotel room, the girlfriend would have come and taken you somewhere and you would have vanished forever, is the fear that Border Force had.

Just FYI if you have a green card you don’t need a transit visa for the UK, it does seem on the face of it that being detained for not having a transit visa was wrong.
[OP being outside the airport is more complicated. As I recall, if you need to change airports (such as in at gatwick and onward from lhr) you can leave airport as long as onward flight is within 24 hours, if not I don’t think you can leave airport, unclear of OP’s specifics, but anyway UK immigration issue shouldn’t affect this. ]

That's great, because we have seen many on here that should have been given the 2 yr GC but instead got the 10yr card. They didn't remove conditions and later found out they had a mess to clean up. 
The other issues I do not see any problems that would result in a denial. Will they ask questions - maybe but you can just tell them the truth and it should be all good. 

Way too much irrelevant information in your post. Next time ditch the personal stuff, no one but you cares. None of that will be an issue. Immigration issues in other countries due to immigrant intent is of no interest to USCIS. You said you’re applying for naturalization under the 5 year rule so your relationship to your ex wife is not an issue. You’re worrying over nothing. 

The UK student visa/transit visa stuff won't be an issue in terms of an approval for US naturalization---just make sure to disclose the overnight detention in your N400 application, and include a written explanation.
 
There may be a bit of scrutiny surrounding your initial green card as the IO sorts through your file, because the divorce happened only a year after receiving it, however your marital status cannot be used as a sole reason for a denial (since you are applying under the 5-year rule).  Generally, the N400 is also a last-ditch attempt to ensure the GC was initially properly approved as part of their overall adjudication for your application.