Unfortunately SRK is doing a server migration right now so I can't give you links. It should come back up later this afternoon. There are a bunch of useful threads stickies in the newbie dojo.
There are a lot of things in fighting games that aren't intuitive. Execution wise, it's difficult to tell where you are having issues without knowing what you're failing at specifically, though the largest bane of new players tend to be links. One general bit of advice: the trial mode combos aren't often ideal. Check the character specific sections in SRK for bread and butters (bnbs) for your characters. The key prt of developing execution is doing it in training mode with input display on, so that you can see where your input errors are. If you find that you can pull stuff off in training mode but can't in real matches, don't worry, it's perfectly normal. You'll improve over time.
As far as your questions:
1) playing the computer isn't useless, but it's pretty close. The AI is easily exploitable by things a real player would never fall for and easily deals with mix ups a real player might struggle with. If you want to improve, play real people. By the same token, local games are better than online. I strongly encourage you to use the regional matchmaking section of SRK to find some pals in your area.
2) the best way to fix bad habits is pretty much the same thing you should do to develop good ones. Make goals. Try to meet them. In your particular situation, don't worry about wins or losses. Play matches where you don't allow yourself to do random cannon drills (or whatever). Your metric for winning or losing should be whether you meet your goal, not whether you actually win or lose. After you've broken the habit, go back to trying to win.
3) both. If you can't execute you can't do damage or defend properly. If you don't understand other characters, your can't attack safely, defend correctly, and you miss punish opportunities. That being said, as a new player, I would focus on three parts of execution: anti airs, punishes, and hit confirms. Matchup knowledge is something you can learn organically to a degree, or look up information when you fight a character you're stumped on.
If you have anymore questions, fire away.