The OP didn’t limit it to America. At least not in all of the questions.
Apply directly to the forehead. :smack:
For most photographed worldwide, I doubt it’s either the Taj Mahal or the Great Pyramid. The answer, whatever it is, will be partly a matter of raw visitor numbers and, although vast numbers visit Agra or Giza, even vaster numbers visit places such as Paris, London, New York and the various outposts of the Disney empire. While one might quibble about some of the details, this list gives a sense of the numbers involved - the Pyramids are only at no. 47 and the Taj Mahal at no. 50.
As for the most painted building worldwide, I would be astonished if it wasn’t either the Colosseum or the Temple of Saturn/Arch of Septimus Severus. All those eighteenth-century vendute surely gave them an unassailable lead on that count.
If we define a “building” as a structure that has to be useful for something other than just standing there ornamentally, then the Eiffel Tower is not a building either. Nor is the Lincoln Memorial, nor the Washington Monument. (But the Taj Mahal is, because it does have a function, of sorts: It’s a tomb.)
By that criteria, we have to exclude Motif #1 as well, as its sole purpose is to be the subject of paintings and photographs. I’m pretty sure that not a single fish was gutted inside of it since before the 1930s.
I’ve never been there, but I believe the Eiiffel Tower houses a busy restaurant. If so, it’s more than a pointy tourist attraction.
Concur - it’s a functional building - not just an ornament.
But I think I’d grant that status even to structures that aren’t much more than a tall viewing platform - if it’s designed so that you can enter it and do something (such as climb to the top and admire the view), it’s a building.
Some mainly-visual things, such as the Washington and Lincoln monuments in D.C. and the Soldiers & Sailors Monument in Indy, have museums in the base of the spectacular part. The arch at St. Louis has a museum about building the arch, and also an extensive museum about Lewis & Clark’s trip to the west coast and back. Sure, you can take a tram to the top of the arch, but if the tram is sold out for the day, and you don’t have a ballgame to catch, you can spend a day in the museums. The gift shop has lots of books and arch souveniers. Sorry, no CDs by the Archies. 
As a Brit I’d say the Capitol building as it is always shown as the backdrop for t.v. news items from Washington.
If we’re taking any printed or produced image then I think it’s GOT to be The White House. Just the number from the Bureau of Engraving & Printing alone show that the twenty dollar bill has a print run around 80,000,000 or so since 1980. And that would be in addition to all the times it’s depicted in all other art forms (hell, just one week of Doonesbury might do it!).
Note that the one dollar bill NUKES the print run of any other bill, though. George Washington is likely the most printed face in the world. The only one I could see rivaling him would be Jesus and I’m not sure that would really get the job done.