I don't have a touchscreen, so I can't speak about that.
For the battery, it doesn't matter if you put the device on stand-by or not. Not even turning it off the whole time would matter. E-ink only draws energy when the screen gets refreshed. And that's when you go to a next page. So, if you leave the device "on", or on stand-by or "off", if you don't refresh the page, you don't draw energy.
(naturally, a battery will drain by itself, nothing can be done about that, at least, not with the current battery technology
...)