No hot water when cold is turned on elsewhere
With the new diagram, we can ignore A&amp;B as they are part of the heating loop.

As for upgrading the 1/2" pipe feeding the water heater, yes, that should be possible, though it may not make much difference if all the hot water for the house is still being sent via a single 1/2" line after the water heater. Now, if you increase the pipe size to the water heater and provide individual PEX from the water heater to the fixtures, you should see some improvement, but it may also be limited improvement if the cold water is still being supplied from the 1/2 pipe in (or coming out of) the wall here. If you can increase the pipe size all the way to the water meter (or actual cold-water entry from the meter), that will help more, but a shorter section of 1/2 pipe is better than a longer section of 1/2 pipe if you cannot get all the way back to a full-sized feed line.