The series is based off a movie, which is based off a book, which was a fictionalized account of life at the actual 8055 MASH unit during the Korean War. The series plays a lot of the movie's more racist/sexist/unprofessional tones down, which itself DRAMATICALLY plays down the extremely racist/sexist/unprofessional antics of the book, which itself were *slightly* played up by the authors (who were the basis for the book's VERY DIFFERENT from the series Hawkeye and Trapper--Hawkeye for instance was a staunch republican, who said in one of the sequel novels "I'm going to go down to Berkley and kick the s**t out of a few liberals"--purely because the author hated the series' version of Hawkeye.)
Were the nurses anywhere as hot? Probably not, but literally no one cared. They were treated even more like sex objects in the book and in real life (it was the 50's, and you had a bunch of horny docs doing meat grinder surgery for days on end with nothing but bad food and nothing at all to do for weeks on end in between. It happened.) Heck, the book pretty much depicts Trapper as a sex offender--he got his nickname after being accused of trapping a fellow student in the bathroom on prom night.
How much drinking was taking place? Probably a lot more than even the authors cared to admit. Alcohol may have been contraband, but war makes alcoholics out of the best men. Both the docs and the nurses needed to be boozed up just not to go nuts at the horrors they witnessed. If you want a vague hint of how nasty the injuries they dealt with were, watch the movie (or read the book). The movie is rated R for a reason.
Did the personnel really fraternize so liberally? Yes, and they behaved even more outrageously than in the movie and series. The fact is, the war was a meat grinder, and they had a lot of trouble getting doctors. So even a p***-poor doctor could get away with nearly anything, and the MASH units were pretty much free-for-alls whenever they weren't in the OR. Take a look at the movie sometime and see the stuff the characters pulled off in that--a lot of that was based on things the authors either did themselves or saw someone else do. (Radar probably wasn't really psychic though, but chalk that up to rule of funny).