Some engines, if they are running really rich, will actually spit fuel out of the carb throat up in to the air. If that's what is going on, then it's not a problem at all.

This is most noticeable at low throttle (I'm not sure I've seen it at high throttle, but I've really seen some engines spit at idle) because the airflow down the carb throat is not enough to suck in all the fuel (and, of course, the intake port is closed a good part of the time, meaning no airflow), but the backpressure from the muffler to the tank is shoving fuel in to the carb. So the fuel comes out of the spraybar and can't go down in to the engine. So the prop blast throws it up and out, where it gets on your hand as you reach for the glow ignitor.

A little fuel or oil on the flywheel (the black thing behind the spinner, pointed to in your 4th picture) isn't necessarily a bad thing. And a little leaking of stuff while the engine sits is also not a bad thing. All my engines leak a bit when they are sitting because I store them nose-down, and any residual fuel or after-run oil will leak out the front bearing. The spots on your newspaper are about what I'd get from some of my engines when I store them. (I often wrap a papertowl around the engine to catch leaks, espeically when the wife is watching)

As for getting the flywheel off, I'm not sure how the Evo holds it on there. Differnet engines do it differently. Some use a key (OS does this), so it would just come right off. Some engines use a tapered cone, which makes a rather tight fit. You might have to use plyers or heat the center of the flywheel to get it to expand. Some actually use an interference fit, so there is no way you can get it off with out using heat or a puller. Unless you really need to get it off, I wouldn't bother. I'm not sure I see a reason here to be going there.

Ok, I just realized I didn't see something in your posts, so I gotta ask:

Does the engine run fine? Reasonable amount of power, idles ok, etc? If the engine runs fine, you don't have a problem go fly. Don't worry about a little fuel or oil getting thrown around, these engines are actually fairly messy. If the engine runs right, then you're just seeing "normal" mess.