How many times does one have to state this?
Spontaneous generation: In a short time, in a small sample...
Simple chemicals -> Insects
Abiogensis: In many, many orders of magnitude more time, in a sample the size of planet Earth...
Simple chemicals -> polymers -> self-replicating polymers -> hypercycles -> probionts -> prokaryotes -> eukaryotes -> colonial eukaryotes -> simple chordates -> arthropods -> insects
Who cares what your dictionary says: This is how *scientists* use the term. Deal with it. Heating material in a small flask and letting it sit for a little while doesn't even remotely discuss the latter case. Not even *slightly*. If you disagree, please explain how it does, instead of just asserting.
As to your mother's jigsaw puzzle, pieces are incapable of connecting just by being shaken, unlike chemicals in the real world. If pieces could connect by being shaken, and connected forms were notably more stable than disconnected forms (both like real life), yes, your mother's puzzle would get completed just by shaking it for long enough. And, to make the analogy more like real life, there would have to be billions of ways the puzzle could be solved.
As for chirality, life *will* work when on the opposite chirality - only if everything is that other chirality. You simply cannot *MIX* chiralities. If a hypercycle ended up creating an incorrect chirality compound, that hypercycle would fail. Once we get to the around the hypercycle level, you're locked into whatever you start with, and producing incorrect chirality proteins means that you're selected against.
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"Illuminant light,
illuminate me."