1) File Sharing:
File sharing across the Internet often can be blocked by routers on either end, though, or complicated by shifting IP addresses. So moving your photos to a cloud-based service such as iCloud's PhotoStream, Flicker, etc,, if that would be at all practical, may be a better option.
2) ARD would be overkill. If you just want to get access to the files, just set up file sharing. If you want to take control of your home Mac, the built-in screen sharing would be sufficient, though a service such as LogMeIn is usually easier to maintain.