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Your description in #2 is only partially correct. Evolution describes the process but the original starting need not be a single cell nor even a cell.

Correction noted and accepted. The comments in #3 are wrong. Evolutionary theory makes no claim that "new" life has or has not occured.

Please note the parenthetical expression in #2, i.e., (with no comment on how such life originally came to exist)

Summary #3 is pointing out that, in fact, the theory of evolution does not address the origin of life of which it purports to explain the mechanism of change. This lack of comprehensive explanation in the theory of evolution leaves open the possibility that the originating phenomenon of life may be continuing to operate.

There simply is no record of other "Trees Of Life."

Please note, as the old saying goes, that lack of evidence is not evidence of lack. Consequently, such an assertion is not logical proof. However, to the main point, I have posited no replacement theory for evolution, only noted what seems to be a lack of comprehensiveness in addressing all observable data, i.e., life exists. Therefore, it came from some source.

Current evolutionary theory (using data from geology) deduces that conditions are different now than in the pre-Cambrian.

Note this was specified in point #3. i.e., Of course, this criticism is subject to the objection that initial conditions are impossible to recreate, ...

Number 4 is also wrong. The predictions of evolutionary theory are falsifiable even if speciation occurs through drift.

This may be one area where additional detail is required. Perhaps I misunderstood. However, as “genetic drift” was explained earlier on this thread by another poster: Genetic drift is a stochastic process in which the frequency of alleles in a population changes due to chance fluctuations in the percent of alleles passed on. . Stochastic processes and chance fluctuations are random operators. If the concession is that alleles (and ultimately genes) are randomly passed on, then without a limiting factor, there is no reason that “drift” cannot randomly create new families, classes, phyla, etc. If the mechanism is conceded to be purely random, any result (even beyond 10 or 12 sigma) is mandatory given enough time. Therefore, nothing is deniable or disprovable. It is the same as saying “Chance did it” (equivalent of saying “God did it.”)… or did I misunderstand?

Number 5 is also false. Speciation with bacteria were observed in the 1950s.

Again, note the parenthetical expression in #5: (Admittedly, contrary arguments can exist but must be muted by the failure among experts to agree on exactly what constitutes a species as well as the fuzzy definition of species.) The fact that there is disagreement on what constitutes a “species” has been noted by several posters (quoting expert sources) on this thread. Consequently, merely asserting it so does not resolve the dispute. In any case, the point is that beyond whatever constitutes a species, nothing beyond that such as genus, class, phyla etc., has been observed.

Summary #3 is pointing out that, in fact, the theory of evolution does not address the origin of life of which it purports to explain the mechanism of change. This lack of comprehensive explanation in the theory of evolution leaves open the possibility that the originating phenomenon of life may be continuing to operate.

Yes, and why is this a problem?
New life may indeed originate abiogenetically even today, however the conditions have changed drastically.
Today, our planet is replete with life and any organic compound is a convenient food source, so the chances that it's swallowed up by already existing life forms before you get some primitive cell are pretty high.

If the concession is that alleles (and ultimately genes) are randomly passed on, then without a limiting factor, there is no reason that “drift” cannot randomly create new families, classes, phyla, etc.

First of all, it isn't a concession, it's statement of an observation.

Secondly, it ain't gonna happen. For the third time genetic drift has its most major influence upon neutral alleles that are not subject to natural selection. In order for evolution to a new phylum to occur solely by genetic drift, the population evolving must be completely free of natural selection. This is a literally impossible state of affairs. Natural selection and genetic drift are inescapable phenomena. Genetic drift influences chiefly neutral alleles, but natural selection drives the innovation necessary for major physiological changes.