Soon, people with much more experience will give you their feedback. Until then here's my trey cents...
That clutch lever is obviously outdated, replace it and the cable, search above for 'proper clutch adjustment' etc.
I put a few capfulls of Seafoam in my bike after it sat for a year or two. I believe it helped, but can't prove it. One capfull in every tank from now on too.
That fuel line wire is inappropriate, replace it with a proper hose clamp for .35 and don't catch on fire
I can't speak to the chain link.
The tensioner is not exactly the same as mine, but those look like stock fasteners to me.
A tensioner on the pedal chain is something people do to take up the slack when it's difficult to align the rear wheel due to differences in chain lengths.
Your drive chain must be matched up as perfectly as you can get it, or it will come off while you are riding. Looking from the rear of your bike, make sure that both your drive chain and pedal chain are in a straight line around both sprockets in the rear, and in the front. Be patient, it's important, but it sounds like your running fine now.
Have you cleaned and oiled both of your chains? Search above for 'chain lube' etc.
That was a great deal, and with just a few more bucks, you should have a dependable runner- congrats!