You can make the battery last longer even at home. Check this story (http://pogue.blogs.nytimes.com/2011/05/23/four-ways-to-make-your-battery-last-longer/) for some tips aimed at iPhone users, but most can be used by the Android. The comments offer more suggestions. Turning off things that use power - push services, notifications, even WiFi if you aren't using it - seem to help a lot.
On the trail, put the phone in Airplane mode (no wifi, no cell service), and turn it completely off when not using it. When you want to write an entry, turn it on, but leave it in Airplane mode while you write, then turn it all the way off again. Every few days, when you think you might have service, you can take it back to regular mode and upload all your journal entries. (I think Postholer takes email updates, right? That would be easiest, I think.)
For power, yes, I have asked politely at stores and restaurants if I could plug in my camera or phone charger. I've never had anyone say no, but then I am always a customer (i.e., buying something.)
I've had a regular cell phone (not a smart phone) on the trail for up to two weeks with no recharge, and only a few texts or a phone call ever day or two, but totally off the rest of the time. It still had five bars of battery life at the end of the hike. I would expect my new iPhone to last at least a week under similar conditions, based on how well the battery lasts when it's on all the time at home.