That's the earlier style petcock without the sock type filter, so you're ok. It's hard to tell from just pictures what they did to the bowl. You shouldn't need a new one as long as it's holding gas. You'll most likely want new rubber parts for it though. Order them, but you can probably put it back together without leaks for now. When you put gas back in, start with just a little and make sure it's not going to leak.
That screen comes out and you should be able to see through all the holes and clean it. You should be able to understand that when the petcock is in the ON position that fuel is delivered through that tall pipe. Inspect it for cracks while you have it out. If it is cracked, you will be able to go longer in the ON position and you'll have less reserve miles once you switch. If you do find it's cracked, you can solder it.
And you should be able to understand now how the reserve setting works.
I didn't read every detail of today's posts, but the clutch lever should be an easy pull when everything is right. No need for a different lever. You might want to lube the actual bolt that holds the lever on if it has rust and crud in there. You should be able to do it with one finger.
As far as cleaning your tank, old gas turns into what I've always called varnish and has a particular smell(think of the old cars you've been around), if it smells like gas has turned to varnish in the tank, I'd put some Seafoam(from Autozone, Advanced, O'Reiley's etc.) in it with some fresh gas and let it sit for a few days, then drain it and rinse with some more fresh gas. I just dumped some Seafoam into my tank, then a week later had to re-clean the petcock and carbs because the varnish all let go and deposited itself into them.
The danger with removing the jets isn't scratching the outside so much as crushing the hole inside and changing it from a round hole into an oval.
I too think you're going in kind of deep pretty quick. I'd concentrate on getting it running well, then move onto other systems. As long as you can handle keeping it straight, ok, but before you know it, you could have just a pile of parts in the garage.
