1. When you enter on the K1 you have 90 days in which to get married. If you don't get married in the 90 days, you have to leave. You can choose to get married on the 89th day if you want, you're OK to be there the entire 90 days. You should apply for AOS as soon as possible, as you'll become out of status every day after the 90 days. If you have no intentions of AOSing, you should leave before 90s of your US entry (not 90 days from the marriage).
2. You can travel after the wedding once you have filed AOS and your Advanced Parole (AP). AP is needed to allow you to leave the US without abandoning your status. If you leave the US before you get AP, you'll be deemed to have abandoned your AOS and have to start all over again with a new I-130 for CR-1 visa, filed remotely (which'll take you another 8 - 12 months). You won't be able to do multiple entries on your K1. The K1 is good for 1 entry only. You cannot leave before you file AOS and AP. I can't stress this enough.
2.1 No. You can't leave the country for a honeymoon abroad. If you want to honeymoon immediately, do so in the US or in a US territory. Or wait until you have your AP.
3. No. You must AOS while you're inside the country on the K1. If you don't want to AOS, but you do marry then leave, you must file the I-130 for CR-1 visa (or IR-1 if you file after 2 years of marriage).
It sounds like you don't want to move to the US after you marry. In which case, the K1 is somewhat a waste of time. You can marry legally NOW on VWP, so long as you leave the country afterwards when your VWP stay expires. Then you'd file the I-130 for CR-1/IR-1 visa when you're ready to actually move to the US permanently.
The K1 path is really for those with the intention to marry and immigrate. You don't want to immigrate yet, so you don't need to get the K1.
You can go to the US in May, marry, leave within your allotted time on VWP. Then, a year or so later when you want to move to the USA, you follow this guide: http://www.visajourn...tent/i130guide1
What you may have read is people being warned not to marry and adjust their status without the K1. Entering the US on a tourist visa with INTENT TO STAY after marriage is visa fraud. Simply entering the USA to marry and then leave is not.
Edited by lost_at_sea, 26 July 2013 - 05:58 AM.