Yes, but you'll need to tell your other views which model to use, as per the answer above. There may be better ways (I'm wondering if a simple second model that just inherits the other one may be a tidier approach), but I tend to use JModelLegacy::getInstance to get access to a different model's functions if I need to do that.

Have you turned error reporting to developer mode? (Under configuration in the admin) This can often help identify problems.

I meant use phpMyAdmin, or whatever your hosting has, to access the database directly outside of Joomla. There are some database management extensions for Joomla to do it in the admin, but I don't know how good these are.

320px is the smallest you have to worry about - mydevice.io/devices

Read up on the difference between modules and components. It looks like you could do most of that with modules, which are far simpler to build.