What a nice day! Congrats on your first solo sail. The DS is definitely a boat that lends itself to single-handing. An observation, meant in the spirit of teaching - trim your sails! IN your video of going to windward, you should sheet in both your main and jib about 2-3 inches (till the windward side telltales lay flat). For your downwind video, congrats on sailing wing-on-wing, it's not easy to do. You could probably have let the sheets out another 4-6 inches for both main and jib, though, You want to "spread your wings" as much as possible - the jib just short of collapsing forward and the main almost touching the shrouds. Admittedly, going dead downwind it's all "style points" unless your racing, not hat much speed difference. But upwind, learn to steer and trim by the tell-tales, Greenlake has a very good explanation in his " Basic Concepts and Techniques" thread.
Another tip, for the future. I'll assume by the fact that you were videoing and steering the boat at same time, that you had your main and jib sheets cleated down. Fine for that beautiful calm day that you had (I'm jealous!). For stronger winds, you'll want to hold your sheets in hand to ease/hike/trim as needed. In other words, you'll need to let the sail out to avoid capsizing! Now, I'm always advising folks to walk before they can run, so don't go out in a half-gale tomorrow, eh? Work your way up to it. But use these lower-wind days to practice. Hold the mainsheet in hand and go thru a couple of tacks, get the feel for it. Advanced - hold both main and jibsheet in one hand and tiller in the other , learn to juggle all three. Tip! hold your tiller extension like a microphone. Pulling in big lengths of mainsheet (like when you're going from a reach to close-hauled) is especially fun. I've been known to use my teeth, although the proper way to do it is with coordinated movements of your tiller hand - grabbing the loose lengths of sheet, sawing the extension back and forth without affecting the angle of the tiller. Look at online videos of Laser or Opti sailors and you'll learn how. Do you need these techniques for light wind days? No, of course not. But it's good practice Also, seriously consider investing in ratchet blocks, makes single-handing in higher winds much, much easier.
As for self-steering, I use GreenLake's bungee setup, works a treat! Try it, it's a great help to have the tiller "park" for a moment as you reach for a beer...

Best,
Tom