You seem to have a good sense of framing - as I see in the first few outdoor photos. You don't need a DSLR to make photos at this point. Use your camera whenever you get the chance and you will start learning a lot more.
If you really want to learn more and improve your skills in photography, just go out and shoot. Sure your "family digital camera" may limit you but learning to work around those limitations is a great way to learn. Looking forward to your future shots.