Dave Mitchell - MSFT
I'm going to see if I can find some time to blog a few details I can share about the contest over at the XNA team blog over the next 24-48 hours...
Now on to your questions, I don't have the types of answers you might be specifically looking for but I do have a couple of suggestions.
1) You can continue to develop your game on a Windows PC/Laptop while traveling. When you get back, you can then focus on making it work on the Xbox 360 if you like. Speaking from personal experience, it is no fun at all to lug around so much hardware while on the road. My back hasn't fully recovered yet from a month of my lugging 2 Dell XPS laptops and a console around the US and abroad.
2) Xbox Live access works across the Internet so as long as you have access, you should be fine. You'll be pinging the US servers from significantly further away but it should work.
3) Networking cables and jacks seem pretty universal so I'd think you're fine there. I know you will be in Japan as that was one of my destinations last year. The places I stayed while in Japan also happened to have standard 110v plugs which was perfect for all my hardware. Not sure about where you're going so check with your hotel or other place of residence while in country. They can help you out with definitive answers.
As for the contest timeframes, all I'll say is that everyone should have plenty (TM) of time to work on their entries. You'll have more than a month to complete it. For those who are on the ball and have already been working on their games, you have that much more of a headstart and likely more time for fit & finish - the stuff that can really set your entry apart.
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Updates at http://www.dreambuildplay.com will be live within the next week. What started off as a fun idea to give all our XNA Game Studio Express fans something to do has grown to be something significantly larger and more interesting. I'm fairly certain you guys will appreciate what has been assembled.
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So your call really as to how much "Globtrotting" to do but definitely have a lot of fun while doing it by jamming on that XNA Game Studio Express game lurking in your thoughts!
--dave