I think prime is a de-chlorinating product. You shouldn't need it with a properly maintained RO/DI.
Are you on city water? If so, which city? Chloramines are used by a couple water supplies in Michigan can be more difficult to remove (DWSD does not use chloamines). Typically, the last step of the TO/DI is activated carbon and that is where much of the chlorine and chloramine removal will occur. The interesting thing about chloramines is that they are formed by the water supply by intentionally combing ammonia with chlorine. They have an advantage for the water system in that they last longer than free chlorine. But after a long period of time, they eventually can disassociate and leave behind ammonia....which quickly converts in an established tank to nitrate. Obviously this is not good since that is one of the reasons we do water changes in our tanks in the first place. But you shouldn't have a problem as long as you change the carbon as recommended.
As for storage, I have seen some posts regarding certain containers leaching phosphates into the water. Although, I'm not sold that this is at the levels of being a problem, it does make sense. RO/DI water is very aggressive. It has been stripped of it's minerals and is looking to reattain chemical equilibrium. So anything it comes in contact with could have some degree of reaction (it is still water so there isn't a violent reaction).
I think John means a TDS meter to verify the quality of your RO/DI?