Questions about radiator/engine flush and running water or coolant

[Houston Ben]

Hi all,
After messing with my new intake for a/c and such I realized I hadn't changed over to coolant yet so I have a few questions.

!. Can I run just tap water? This is what I have been running and seems to work and cool fine.

2. If NO to #1, what is the best method to flush the radiator and engine of all the brown water without using harsh chemicals or taking it somewhere?

Any other words of wisdom?

Thanks!