Morale decreases as population decreases. So does the effective value of your morale buildings. This is intentional, to prevent massively populated planets. Your homeworld has low morale because it caps at 16 billion and all your other planets cap at 8 billion (before farms). Due to the morale issues above, there is never a reason to put a farm on a homeworld, and no more than one on any regular planet (there are exceptions, but for a beginner this is close enough). DO NOT USE farm bonus tiles, especially the 300% ones. Ideally, aim for 12-16 billion people on PQ11+ worlds and stick to the 8 billion cap for anything PQ10 and below.
Note that tax income is based on the square root of population, not linear increase. This means at 13 billion you are giving up about 25% of the income you could get at 20 billion, but need fewer morale structures and can easily make up that 25% by building more stock markets.
Edit: Also my homeworld and few worlds with bad moral are all pretty much population capped and they are whining about population so wtf does one do. Not like I have an "slaughter 1 billion of my own people" button (hmm thats an idea for GC3).
Being pop capped is a good thing, as it means your morale won't be getting worse. For the other planets, I'd suggest getting rid of farms on bonus tiles (make sure to rush build a non-bonus one, then demolish the bonus farm on the same turn to minimize population loss) and just demolishing farms on any planets that exceed the guidelines above. When the farm is gone, any population above the cap simply disappears when you push turn.
For your homeworld, get rid of any farms. If nothing else, turn your homeworld into a transport spam factory. If you build them fast enough, you will use population to load them faster than they can regenerate. Or build transports elsewhere and only partially load them, then fill them up on your homeworld.
I can't help you with the governor problems, I've never used one.