"How did the first lifeform begin?"
Are you referring to organic life on Earth or Cosmic "Life" ?
In either case I don't know.
"If it began spontaneously, why isn't there evidence of complex precursor molecular structures in thermal volcanic ponds, etc. somewhere?"
Can you expand on what you mean by "
spontaneously".
For example if someone drives or wades into floodwaters and is swept away and perhaps even dies, is that event spontaneous or the inevitable result of well known Laws acting in those conditions ?
Also are you confident that there is no
complex precursor molecular structures in thermal volcanic ponds, etc." anywhere .... which would mean all those
thermal volcanic ponds have been examined for this very rare development ?
"
Why did early life split into two entirely different evolutionary paths, plants and animals, with plants having the ability to photosynthesize food for animals from the sun's energy, resulting in an elaborate self-sustaining ecosystem, all supposedly spontaneously?"
Much more complex and interesting than just those two paths. There are "kingdoms" such as viruses, bacteria and fungi which don't fit either of those paths. Not to mention the geological, and Solar/Cosmic processes that govern the "life" and "evolution" of the Earth.
"Why have we had so many "lucky mutations" compared to our primate cousins: bigger brain and associated blood flow, ability to communicate by complex speech, dexterous hands, etc ?"
I don't know and can't say whether they were lucky mutations or a chance combination of all the Laws and processes and their complex interactions that constitute "evolution", or even intentional intervention by "higher powers".
Perhaps they were the result of the OT Jehovah experimenting at projecting Himself into lower levels by creating organic beings in the "image" of Himself and Higher beings.
If so, still work to do there and if you listen carefully it is still possible to hear a constant background sigh of "Good grief, what was I thinking !"
"
Why are the extraterrestrials so coy about showing themselves to us and seem to have been mainly observing us from a distance for millennia,"
They aren't coy but sensible and interested to see what happens as a result of the mistakes made by Sol's Higher Powers when trying to adapt Humans to serve several different requirements. Unfortunately for Humanity, direct and global intervention is beyond their paygrade and would have to be a direct request from said Sol Higher Powers.
There is also the possibility that Sol Himself is still being "counseled" by His Galactic "God".
In the distant past when Aliens moved freely and interacted with Humans, the unintended consequences required a messy blanket no public contact order which is only now being reviewed.
"and why haven't they subjugated and enslaved us ?"
Why would they do that ? It's a strange and peculiar practice that only exists on Earth.
"Could John B Calhoun's 'Universe 25' mouse "utopia" experiment provide a clue? https://en.wikipedia.org/wiki/Behavioral_sink.
Could it be that we are laboratory test animals in an elaborate experiment being conducted by a higher life form? "
I suppose elaborate experiment is one way of putting it.
So, a few take away ideas.
Life on Earth and it's evolution is a fairly distant result of a series of Universal Laws enacted as part of the original "Creation". This creative impulse passes down through successive levels each adding it's own additional laws and "Higher Beings"
Planets are almost at the lowest level in this chain and have a complex series of laws and interactions between those laws. They are ruled by their Father/Sun which is God at this level.
"Life" at this level is governed by the Sun and it's "incubator/Mother" ... Earth Nature, together with all those higher level laws mentioned.
Humanity is part of Nature and has an involuntary and particular role to fill. This is to do with the transformation of matter into other matter and energy, as an organ of perception and to compensate for certain mistakes that were made during the evolution of life on Earth.
At present these requirements are only just being met by a vast increase in numbers with corresponding elevated levels of hysteria, emotion/fear and misuse of sex energy ... rather than a voluntary conscious quality of living.
When Nature decides Humanity is no longer suitable, the usual "culling" will occur or Humanity will be replaced.
However, apart from this general purpose of Humanity, there is also the possibility of an "individual" role.
Taxes must still be paid to Caesar, but through conscious hard work it is possible that Caesar can be paid with some left over.
.