Alright, take a deep breath. Your first car is a big responsibility but you don't need to freak out about it. These wonderful little cars will drive hundreds of miles without oil or coolant. They keep running even if they need head gaskets, main bearings and new distributors. Yours isn't going to explode in the next two days, so you have time to figure out what's going on and fix it.
If you overfill your coolant reservoir tank, it will bubble out like that when the car warms up. The coolant at the head gasket could be a leak from an oring higher up so look for that. The running issues sound like you got a crap carb from the yard. It's actually more likely that a carb from the yard will be crap than that it won't. Blue smoke usually means burning oil but it can be hard to tell the difference between black smoke (gas) and blue smoke (oil). Make sure that you are indeed getting blue smoke. My guess is that it's gas from your crappy carb.
You can rebuild your own carb, but you shouldn't. At least not yet. You want to learn on easy stuff first. Carbs, and especially these carbs, are very difficult. Start with oil changes and work up from there.
I'd be very surprised if you have a rear main seal leak. You probably have a valve cover gasket leak which is dribbling down to the bottom of the engine and looking a lot like a rear main leak. Most oil leaks on these cars are just a few $3 - $20 orings or gaskets that are very easy to fix.
The tapping is probably valves. Just adjust them. It's relatively easy, but there is a "feel" to it that will take a long time to acquire. You can try it, but be prepared to do it a few times before finally getting it right.
A head gasket is a major repair and you'd do well to leave that one to someone else for now.
Don't worry about the black piece inside your distributor moving. It's no big deal.
The upshot here is that a good mechanic always looks for the cheap fix before going to the expensive one. Before buying a new carb, run a can of fuel injector cleaner through it first. See if that helps. If not, then move on from there. Spend some time in the carb section of this board. There are a number of incredibly knowledgeable carb members here, so read extensively and then post any questions in that section.
Last bit and then I'll stop.
This is the link to the Honda factory service manual. It's your best friend. Learn it, live it, love it.
Good luck and keep us posted on your progress.
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