Yes - both.
I've also had problems with staff restocking coffee- at just about every place I've ever stayed!
In a pinch, a folded paper towel can be used as a coffee filter, but a good idea to bring some.
I also found using two packets makes the coffee as stong as I like it.
Coffee REALLY STINKS up your luggage, so I double wrap it in ziplocs.
You can get milk in the resort gift shop and keep it in your fridge. the gift shop prices are better thanthe food court's.