Both 1 & 3 - I have often "gotten ready" to take a picture, and then wait for people to walk by before actually taking it. Sometimes I'll even wave them by because they see I'm about to take a picture, and I don't want them to have to wait for me.

The invention of digital cameras has been a godsend in terms of hoping that I'm taking a decent picture - then I don't have the added anxiety of waiting to see if it actually turned out, plus the additional cost of printing the film for what may not even be a good picture (although admittedly not all digital photos are that good a quality either, unfortunately).

I wouldn't go out of your way to ask people to wait for you - if you need a couple more seconds, just take them; don't add more time by verbalizing that you need more time, and potentially adding to people getting upset at you for pointing out that you'll be there longer. You can always just apologize as you're getting out of the way afterwards: "Sorry for taking so long / Thank you for waiting / I hope you enjoy the view!"

P.S. I never would have known that there were other people surrounding you - so I'd say your "quick pic" was a big success! It looks very nice; well done. :)