Sometimes, without you really noticing the lather dries a bit and that is what really causes the burn.

The water does a lot of work, the lather holds the water.

Yes, do a few strokes, if needed (but these can also be the cause of razor burn) and then cool the area quickly with cool water. If you create razor burn, it's similar to any other burn, the longer you wait to treat it the worse it gets.

So, lots of guys use cool water when they get done shaving, but by then a lot of the damage is already done.

Once you learn to shave all these tricks will become useless by the way. A straight razor is the smoothest shave on the planet (once you get it down).