Learn English – Nouns with different meaning in the plural form. How to use them on plural sentences

Only the context can be used to indicate this, together with local knowledge (for example it is far more likely, in my experience, that a "System Log" contains information about one system, not many). However using the prefix "specific" before any of these cases indicates that it is more likely to be singular.

For example:

To find the cause of this system error we need to look in the specific system log.

If you want to know more about the vulnerability, you need to read the specific vulnerability assessment

It is not foolproof, and really only indicates that your target is just one of many such objects, whereas the actual object could itself be a collection. But I think in the absence of other context or local knowledge it would be well understood by a native speaker.

Yes, the former and the latter can have plural antecedents, and plural agreement; and no, they do not change form to reflect this. You can find plenty of examples, in well-edited prose from each of the past several centuries, by Googling. For example, I just searched Google Books for "the former were", and here is the first hit:

[…] intergovernmental specialization agreements and jointly financed investment projects. The former were mainly in support of machine building and manufacturing more generally. The latter were principally designed to shore up the buoyant exchange of Soviet fuels and raw materials for Eastern European manufactured products. [link; emphasis mine]

Edited to add: By the way, I should mention that both of your examples have some problems, but in the first sentence. "The person in the right" and "the person in the left" should be "the person on the right" and "the person on the left". (With a very specific appropriate context, it could be made possible — if a photograph depicts two cars, for example, you could potentially refer to one car as "the right" and one as "the left", and then each person would be "in" one of these — but otherwise it would not be natural.) Similarly, "those who in the right/left side" should be "those on the right/left side" (or perhaps "those who are on the right/left side", but this implies that being on one side or the other is a more significant property than simply a matter of current position).