The port at the bottom of the regulator is to release water collected in the bowl when the air pressure is turned off and drops to zero. It is a little valve that closes, or should close, when the pressure comes on. If you block this permanently and your air has water in it you will probably get problems.
When the spindle is running and for a short while after it stops there is an air flow through the spindle. It should stop a few minutes after the spindle stops.
When the tool changer is operating there is a much larger air flow throuigh the spindle.
You need a compressor with at least 4 cfm capacity to run the machine and it will turn on very frequently when the machine is running.
You should try scanning through the posts in the Haas forum, a few months back there was a similar thread and some suggestions for an moderately inexpensive rotary screw compressor.