Most of this stuff is spot on.
To me, down is just barely harder than sit. You should really do yourself a service of getting your hands on obedience puppy books or taking an obedience puppy class. It's worth it just for the socialization. It's not that you can't do it by yourself, but you'll definitely pick up tips that will make you and your dog better. My 6 month old who I have trained this year is in an obedience class right now. She's the best dog in the class, and the next youngest dog is 2 years old. But she and I BOTH pick stuff up. Even if it's little things like hand placement when treating, when asking to do certain commands.
For specific commands, if you can't buy dvd's or read a book, watch youtube. Watch 4 or 5 videos from different people to see some different approaches.
I like to teach down once they have sit. While they are sitting, put a treat in your hand, then to their nose. In a very deliberate motion, move that treat between their front legs. Some will bob their head, some will lay down. If they don't lay down, then (on the ground), slide the treat out in front of them about 6-12 inches. Usually they will pick it up quick. Start reinforcing the word "down" once they have complied a few times.
You are no where ready for heel. Forget about heel for a while. Work on walking on a leash, having fun, smelling new things. Think how many objects they've never seen before!!! Everything! You should be working on introducing them to new surroundings, people, voices, sounds, etc.
In a few weeks, while walking, while the dog is on your left and walking in a heel position, say "heel" then "good dog" when it's correct. You are starting to let them know where "heel" is. Heel is never pull on a leash and command heel. That is a very big misconception with the command. Like I said, right now you are associating the position with the command, not commanding the position. More later, read or watch some puppy stuff. If you're too lazy, then that's on you. Good luck!
That rug really tied the room together...