Question: What is the picture of women on the walls of the set? Not the butterfly picture, the others.
Answer: Or, you may be referring to Tranquillo Cremona's High Life (A Piquant Conversation), which hangs above the side table.
Question: If Roper wouldn't rent to Jack unless he faked being gay then what made him not suspect the girls of being gay?
Answer: Possibly because in the 70s/80s, no-one would bat an eye about two girls living together, or 2 guys living together.
Answer: Because they've had various boyfriends and dates over the years. How he never noticed Jack had a stream of women coming to The Apartment is another issue.
Question: Who decided to make Chrissy stupid? Watch an early episode like "Roper's Niece" then a later one like "Jack's Pie", So who decided to make her stupid? Some network executive?
Answer: It's also likely a case of "Flanderization", where as the show progresses, the writers zero in on a single aspect of a character that they get the most material out of, and think is the funniest, and expand it at the expense of realism or development, to the point where it is the character's entire personality.
Question: During the first three seasons, all the main cast appeared in every episode (except one without Joyce Dewitt by season 3), but it seems once Suzanne Somers left the show, episodes had some cast members absent on a regular basis (mainly Richard Kline and Don Knotts who both only appeared in selected episodes in the later seasons). Was it a sudden budget cut or another reason for this?
Answer: Richard Kline and Don Knotts were supporting cast members, who could be replaced at anytime. It was John Ritter, Joyce DeWitt and Suzanne Somers who were the star vehicles they relied on to carry the show.
Question: In the second episode Chrissy's mother comes to visit. In future episodes her father comes to visit - who is an actual "father" (i.e. priest). Aren't priests forbidden to be married?
Answer: He's not a Catholic priest. He's a pastor, with the title Reverend, at a community church who chooses to wear a clerical collar. Some people still address pastors as "Father" though. I'm not sure of his religious denomination, but most pastors can marry.
Answer: Yes Pastors can marry... I was asking for Priests since his collar appears to be that of a Catholic descent.
Some protestant pastors wear the clerical collar as well: https://en.wikipedia.org/wiki/Clerical_collar.
Answer: I believe you are referring to the artwork of Alphonse Mucha. On the wall next to the front door was "Feather" (which is one half of "Primrose and Feather"). Above the telephone in early episodes was "Zodiac". Also seen through The Apartment was "Spring" and "Autumn".