I have always been told that you can bring your own soda in moderation...As far as the Diet Coke on board goes, it may not be diet coke. It is a soda card, and they don't tell you that it is specifically coke products. I would ask what they serve on board specifically as they have to tell you. If it tastes bad it could be that it is somewhat flat. That is the problem that I encounter most often.
If you read the frequently asked questions section on their website, it will tell you how much of your own soda you can bring on.