There is absolutely zero evidence for early cells which operate substantially different from modern cells. Conjecture about things for which there is absolutely no evidence should not be taught as TRUTH or as SCIENCE because it is neither.
Classic example of the religious mindset. If we cannot find evidence of something, then it is must be proof of God.
Incidentally, the Theory of Evolution is about the FACT of Evolution. Evolution, like gravity, is both a theory and a fact.
The FACT of gravity is that, if you jump off the Empire State Building, you will almost certainly die. The THEORY of Gravity is an attempt to explain why this is, relating to attraction between masses. If you prefer say that the reason is because God doesn't like people jumping off buildings and punishes them for it, then you are welcome to do so. That is also a theory. Unlike the other one, unfortunately, it has no explanatory power and thus it is not taught in classrooms.
Similarly, evolution is a FACT. The Tree of Life is undeniable. It is proven in five or six different ways - in our DNA, in the fossil record, in morphology, among others. To deny this fact is to deny the evidence of our senses. You may argue, as some know-nothings do, that God put down fossils to test our faith but I sure ain't going there. The THEORY of Evolution, in contrast, proposes a mechanism to explain how it all happened, specifically Natural Selection. Lamarck proposed another mechanism.
You may advance the notion that there's a Great Species-Plopper in the Sky who puts down new species in the fossil record is precisely the same manner as if they transformed from one into the other and then modified their DNA to reflect this. Sounds pretty absurd to me but at least it is in accord with the FACT of evolution.
As for what happened in times for which we have no records, you are quite right to say that anything there is speculation. However, Occam's Razor leads us to believe that the mechanisms by which the world evolved (there's that nasty word again) would have been the same then as now - especially since we now have considerable understanding of the nature of the early Earth and will probably be able to evolve primitive life in the laboratory within ten years.