Unless you want to gum-up the plumbing and filters...I wouldn't add the nutes. Doesn't the manufacturer recommend a capfull of chlorine bleach every month or so to prevent algae? No way to control the uptake of those nutes in your plant, but I'm sure the algae would appreciate the food source though. In my opinion...bad idea in general.

Doubtful the humidity ph really matters unless it's from a toxic source. Not too sure adjusting the water ph is necessary, but there's one way to find out. Run it with tapwater and see what happens. If your water needs to be adjusted...what's in it, and will it affect the cooler? (calcium, lime, rust...) Perhaps r/o water would be better?