It is already a 2.5 inch form factor, so swapping in a 2.5 inch SSD is reasonably easy, once you get all the adhesive separated with the plastic pizza cutter wheel, and carefully remove the lcd/screen combo. If you break this assembly, replacements are currently only available from China directly, and are expensive. I would really consider a thunderbolt external drive instead.
The battery will work fine, even when bent. Severe bands can cause fires, but gentle bends can be flattened out again. Either your motherboard has a problem, or your power button is stuck. Try with the switch connections disconnected, and connect the phone (off) to your computer running iTunes. It should boot normally, I test motherboards out of case this way.