This could be part of future image annotation tools (text/shape etc, my post here).
An interim suggestion - as part of your roll out can you have the enumerators set their camera aspect to 1:1? This will get you the square images. At least on my samsung device, aspect is preserved when set either in camera app directly or in camera app via image widget. You could also specify an alternate camera app in the form (eg Open Camera) and set that to 1:1 so accidentally changing the aspect in their default camera app for other uses doesn't affect it.
As far as resolution, making them very small with max-pixels to optimise size for choice use only means you'd have no larger image for use elsewhere?
I haven't tried this, but potentially you could capture the image ${the_big_photo}, then drop that value as default into another image field ${the_small_photo} with a calculate on it like concat('path\to\',${the_big_photo} and set max-pixels on that one to something low. This might return you two sizes of the image, but potentially won't work unless you can work out the xform path to the captured image to concat to the filename? (like having to prepend jr:\\images\ for defaults from attachments.)