Best scenario: unpaired or paired situation?

I have a few questions, but first let me give you some necessary background of the experiment and the underlying questions.

Basically, the design is as follows:

3 independent repeated experiments across different days using different stocks of a cell lineage (clones);
One factor called treatment with 2 levels: control (inert solution) or a bacterial suspension (1x10⁶) are to be administered.
For each experiment, an equal amount of cells is seeded in 6 different plates, of which 3 of them are treated with control and 3 with bacteria.
This is repeated once a month, with a fresh bacterial solution prepared each time (same cell amount 1x10⁶), although, they have different viability each time, i.e, 70%, 81%, 90% and this parameter is not always measured. It is known that the viability of this bacteria slightly changes the cell's response variable that is being measured: gene A expression, but this difference is not the aim of the experiment (just an unavoidable unfortunate).

Several questions arise from this design:

Is this a paired experiment?
Code:
``````| Control | Treated |
|---------|---------|
| 1.1     | 5.1     |
| 1.4     | 4       |
| 1.7     | 3       |``````
Each row is the mean from the three technical replicates (3 plates) for one experiment. Altogether, n=3.

Does this difference in viability from the bacteria across different observations change the fact that we have the same clone cells being stimulated? This is similar to the scenario where a person receives a treatment and some variable is measured before and after this treatment.
If paired or unpaired, given such a minuscule sample, would you recommend perform a T-test, One-way anova, or a non-parametric test, such as Wilcoxon Rank Sum, Mann-Whitney or Permutation test?
This is very complicated subject since in the biomedical literature we often find such experiments and different approaches to analyse it. Some researchers consider this a paired experiment, others don't. Some use parametric tests (although they usually don't say if the data meet the assumptions of these approaches). On the other hand, others prefer non-parametric approaches, often resulting in a large P-value, given the lack of power of these methods for such a small sample.

Well, I'm understand the pros and cons of this experiment anaysis, but is difficult to convince my colleagues given the amount of discordance in published results. Even from "good" journals, like Nature and Cell, I often see some experiments with similar design and analysis using T-Tests and Anova without even discussing this decision.