Refillable mugs:
The cost for a refillable mug is $5 per day for the length of the cruise, so a 7 day cruise would be $35. You still have to pay the full amount regardless of which day you buy the mug on, so it would be $35 even if it's the Friday before you disembark. The mug is good for one cruise only, some people find it inconvenient to carry them around everywhere you go.
You can get the mugs refilled at any lounge and you can also ask them to refill it at the full service restaurants. You can get any soda drink they have in the fountains. They have Diet Sprite, but it's only available in the cans so you won't be able to get it in the refillable mug.
If you prefer to get a soda drink in a can, you'll have to pay for each one, and it's $1.50 each plus a mandatory 15% gratuity. You'll have to pay for each can of soda even if it's during a meal.
At full service restaurants, you can get free soda fountain drinks during the meals.
Trading Cards:
DCL has trading cards that you can get at various places around the ship. There is a symbol in the daily navigators that will indicate where they will have them, but I think you can ask any of the ship's officers if they have one when you see them walking around anywhere. I'm not sure of the number of cards they have, I think it's somewhere between the mid 20s and 30.
Hope that answers your general questions.