You get married the normal way, just as if you were marryng another American. If the alien is illegal because he overstayed his visa, you would file for adjustment of status after getting married and wait for the greencard here in the states. If the alien is illegal because he snuck into the country, you would file the I-130 then file for the K-3 in his country.
He'd be denied and you'd then file the I-601.
Each visa is viewed under the same criteria, your parents being older and very possibly have been to the UK before could mean they are checking if they complied with any visa they were given then, could be they have no fixed job to return to, so that makes them think a possiblity that they will not return, it could be any number of reasons and ONLy they can answer The dates of travel will not influence them at all, they will tell you it takes as long as it take for them to check, I suggest your parent contact and ask what the hold up is and if they can supply any further information which will ensure they get their decision............
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.