Filtered water is alright, but you'll want to avoid distilled water. It can damage the boiler and your drinks will lack flavor.
#2 How long does it take to heat the water before brewing?
The machine will be ready to brew in about a minute.
#3 Can I connect a water line from my filtered water fountain, not using a water reservoir? Is there a connector for a water line in the back?
No. There is not a connector for a waterline in the back of the machine. The water is in a self-contained reservoir.
#4 How is the milk dispenser cleaned out automatic?
There is a "quick clean" button on the machine which blows hot water / steam through the milk path, but this only cleans the milk path. The milk dispenser still needs to be taken apart and cleaned thoroughly at least once per week to clean out the old milk that gets caught in cracks and crevices of the dispensing mechanism. A bit of a hassle to do this, but it's not a big deal and is explained well in the manual.