How well does the screen/font sizes work? I imagine that if I had the text at a font that was readable without holding the phone 4 inches from my face, I would have to change pages every 30 seconds.
I have a Droid RAZR (4.3" display I think?). The text formatting has a few options. You can raise/lower the font size, choose how it is displayed on the screen (width), and also choose spacing (3 different modes). You do, even with tight spacing/wide screen/small font, have to turn the page often, but it only takes a tap on the screen of the direction you want to go, or you can set it to use volume controls to turn pages. I prefer small text, so I enjoy reading from the phone, and the page turning isn't noticable really once you use it a while.
How much power does the phone app use? For a 2-3 hour reading session, will I need to be tethered to a wall to keep my phone from dying?
Not much power at all. I usually read an hour or two before bed at night, and with the RAZR of all phones, it doesn't wear the battery much at all. This is in combination with using the Smart Actions app to turn things off I am currently not using (4G, etc).
How well does outdoor reading work? Is the text legible on a bright, sunny day?
I can't speak too much to this, as any 'outdoor' reading I do is either on my back covered patio, or sitting in a car. You can control the brightness of the screen, as well as use one of three different color schemes: white background and black text, beige backgroupd with slightly darker text, or black background and white text.