I'm a complete layman here, but it makes me wonder if Neanderthals were bred out of existence more than anything. I heard from PBS Eons that it's conjectured that Neanderthals had greater nutritional needs, and that it's possible hybrids between Neanderthals and Sapiens were infertile for one sex (males I think?). If Sapiens was more adept at gathering resources, it would follow that some number of Neanderthals might successfully join Human communities and survive to pass their genes on to the Sapiens population. If all-Sapiens and blended communities were doing better at survival than all-Neanderthal communities, that would eventually lead to the extinction of the Neanderthals while preserving some of their genetics in primarily-Sapiens descendants.

I do wonder how migration of other groups into Europe that did not have Neanderthal ancestry affected the distribution of Neanderthal genetics in the native European populations. Could that have possibly diluted the contribution of Neanderthal ancestry of some European groups to current levels?

Your first point reminds me of the Ediacaran biota, which appears to contain the earliest forms of multi-cellular life - before even the Cambrian Explosion. What's fascinating is that probably 99.9% of these species died out 600 million years ago, with that small fraction surviving into the Cambrian to establish the forms we know today.