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["...at any moment *hundreds of billions* of favourable mutations will *simultaneously* be working towards fixation."]

Sorry Dude, it doesn’t work like that.

Sorry, "Dude", but it does.

According to the Theory of Evolution, if a mutation takes place, the whole process starts over again.

Um, no. That's only according to your cartoonish misconceptions about the Theory of Evolution. The real Theory of Evolution says no such thing. Where did you "learn" about evolution, a creationist pamphlet?

There is only ONE parent unit involved. (simple cells split, others require male and female)

So... You've never heard of lateral gene transfer or genetic recombination in unicellular organisms, eh? You know, actual knowledge of biology is rather a prerequisite for being able to effectively analyze it.

“hundreds of billions” of cells can’t evolve into the same new type.

No one said that they would. But the point is that hundreds of billions of cells have a hundred billion more opportunities to give rise to a useful mutation, as opposed to one cell.

Only one cell in the “hundreds of billions” can be the parent to an individual new type.

Gosh, that's going to come as a big surprise to these folks:

Molecular evolution perspectives on intraspecific lateral DNA transfer of topoisomerase and gyrase loci in Streptococcus pneumoniae, with implications for fluoroquinolone resistance development and spread
Abstract: Fluoroquinolones are an important class of antibiotics for the treatment of infections arising from the gram-positive respiratory pathogen Streptococcus pneumoniae. Although there is evidence supporting interspecific lateral DNA transfer of fluoroquinolone target loci, no studies have specifically been designed to assess the role of intraspecific lateral transfer of these genes in the spread of fluoroquinolone resistance. This study involves a comparative evolutionary perspective, in which the evolutionary history of a diverse set of S. pneumoniae clinical isolates is reconstructed from an expanded multilocus sequence typing data set, with putative recombinants excluded. This control history is then assessed against networks of each of the four fluoroquinolone target loci from the same isolates. The results indicate that although the majority of fluoroquinolone target loci from this set of 60 isolates are consistent with a clonal dissemination hypothesis, 3 to 10% of the sequences are consistent with an intraspecific lateral transfer hypothesis. Also evident were examples of interspecific transfer, with two isolates possessing a parE-parC gene region arising from viridans group streptococci. The Spain 23F-1 clone is the most dominant fluoroquinolone-nonsusceptible clone in this set of isolates, and the analysis suggests that its members act as frequent donors of fluoroquinolone-nonsusceptible loci. Although the majority of fluoroquinolone target gene sequences in this set of isolates can be explained on the basis of clonal dissemination, a significant number are more parsimoniously explained by intraspecific lateral DNA transfer, and in situations of high S. pneumoniae population density, such events could be an important means of resistance spread.

They seem to be under the impression that gene transfer *can* take place between non-sexual bacteria. What do you know that they don't know? Write it up for us and win the Nobel Prize for demonstrating that lateral gene transfer is actually impossible after all.

The Theory of Evolution does allow the “hundreds of billions” of cell to evolve into many different new types of cells.

That too.

Based on the Theory of Evolution, any specie’s lineage is always traced back to one parent (parents) for each transition. (evolutionary tree)

Sorry, no. That's neither true for species which reproduce sexually, nor for those which do not if they are subject to lateral gene transfer, as a great many are.

According to scientist, we only have 10 billion years to deal with.

Nasa.gov: “A particularly important epoch lies between redshifts of 1 and 3 (from about 7 to 10 billion years ago), when the present-day universe began to take shape.”

Do you get it?

Sure. No problem. The observed and measured rates of mutational novelty are more than sufficient to produce modern life from more primitive beginnings within ten billion years. On Earth, it took only three billion.

The earth wasn’t here 10 billion years ago. That’s when “the present-day universe began to take shape”.

Fine.

How much of the 10 billion years was used up before the earth was even here, and then able to support life?

See above.

So, we have way less than 10 billion years to go from rock to man.

Three billion years, give or take.

We each start out as one cell at conception and turn into a 10-trillion-cell mechanism able to reproduce same.

Yeah, and in only a few short years.

You don’t need a $5 calculator to realize these numbers don’t add up.

You "forgot" to show your math. You just mentioned a few numbers then expressed your incredulity. You haven't done any "adding up" whatsoever.