A:
Easily. You can connect the Moto G to your computer via a USB cable and transfer the photos that way.
It would probably be a better idea to set up some sort of cloud backup, either via Google+ which can automatically backup your pictures to Google Photos, or use a 3rd party app like Dropbox which will automatically back them up as well. That way even if you lose your phone while you're out, any photos you've taken will be saved for you to access.