How long you run without dumping nutrient solution is not a factor in pythium prevention, however your benificial bacteria population should be replenished every 3 - 4 days imo. Nutrient exhaustion is the reason to dump a res. I have reservoirs, albeit large ones, that run for 60 - 75 days w/o...
No. You have a heat exchanger. You feed water in through the exchanger and the output is chilled.
A chiller with a titanium exchanger, such as is used for aquariums is preferred.