How to make a parallel connection between two components when each has its own voltage?
The amount of current that can be drawn from a COM port is not part of its specification.  You would need to look up your individual COM port's drivers and find out how much current they can provide.
Practically speaking, you can pull 10-20mA without trouble, as serial mice used power from these signal lines to power the mouse, and they operated in this range.  To be safe, I'd put resistance in the line to ensure you cannot exceed those currents with the voltages available.
From V=IR, R=V/I = 5.8V/10mA = 580ohm
So if you have 580 ohms of resistance between your power sources and your sinks, you will stay within the range that they are typically designed for.