I took the oil filler cap off while the engine was running today. Be careful doing that because the cap and fan blade are close together. Ask me how I know. With the cap off I could see oil splashing around. If the engine had been running above a fast idle it probably would throw oil out the hole. Is that normal/good?
Yes and yes.
Likely normal, unless your oil level is too high.
The cap is really the breather for the engine when running. That oil immediately under the cap is being slung by the timing gears.
That is a good sign! I check mine every so often. If you see a little water (milky oil)it's just condensation and will go away after the engine is up to running temp.