As far as I understand, one of the main purposes of the eight factor of the Path (samma samadhi) is to clean the mind from impurities.
All factors of the N8P have the same purpose, they just operate on the different levels of coarseness. Their purpose is to first reduce and then completely eliminate creation of causes for the arising of dukkha. Generally speaking, some factors operate at the level of external circumstances, they are about not creating causes of dukkha in regular life. Other factors operate at the level of inner circumstances, they are about not creating causes of dukkha in your mind. The boundary between the two is not entirely black and white, and some factors are kinda both external and internal, but you get the idea. It is the same principle of "discord is dukkha, concord is sukha" applied at all levels. Samma samadhi is the most refined level of this progression from coarse to subtle. What we do on this level is shepherd our own mind to see where we habitually create/maintain discord, and try to stop that and create/maintain concord instead.
There are a lot of criteria that can be used to know whether one method is right or not;
The chief criterion, I think, is whether it's going in the right direction. And the right direction is less discord. It's very simple, really.
how important and relevant is the behavior of the meditator (towards others and in general) as a factor to check whether his/her meditation style is right or wrong?
Since we are saying, it is the same principle applied to everything from coarse to subtle, it becomes super obvious, that if the meditator keeps creating discord at the coarser levels, let alone in their external life, it probably means they do not understand the key principle behind the Four Noble Truths. If they do not understand the principle, how can their meditation be right?
ethical qualities of the meditator ... little to no empathy, prudence or wisdom
It is important to understand that our "worldly" ethical qualities are not 100% identical with Buddhist skillful qualities. They match 95% of the way, but not 100%. The Buddhist skillful qualities serve single purpose, progressive reducing of discord until complete and perfect "Nirvana". The worldly ethical qualities serve the purpose of reducing the discord between the members of society pursuing their individual worldly objectives. The principle is the same but the end goals are slightly different. This is why you can't simply assume that if someone is not perfectly ethical by the worldly standards, they are a bad Buddhist. They maybe optimizing their behavior for the pursuit of Enlightenment and Nirvana vs. being a good citizen. That said, because both objectives involve management of causes of discord, you can't really pursue one without taking care of the other, at least 95% of the way.
So, regarding empathy, someone may show little empathy to a Wall Street banker crying over his lost fortune, or a lady crying over the wrinkles around her eyes, because these are not the objectives leading to Nirvana.
As for prudence and wisdom, in Mahayana it is assumed that the practice of creating no discord at some point necessarily leads to an understanding that all conceptual constructs are simplifications. When someone understands this point (called "Emptiness") very deeply, it very certainly manifests in their worldly behavior, making them less prone to taking one-sided positions, and more inclined to be prudent, nuanced, multifaceted, and analytical, which are the characteristics of wisdom. So in this sense, it is absolutely expected that someone with a decent level of Buddhist realization should show some amount of worldly wisdom as well. Mahayana even has an official term for this. It's called "coemergent wisdom" (sahaja-jnana).
The two takeaways from all this are: 1) not creating causes of discord, and 2) seeing through conceptual simplifications -- are the two qualities that operate along the entire N8P from ethics to meditation.
In summary, you are right to assume correlation between one's meditation and ethics, and as long as you understand the principle underlying both, and all the caveats I described above, you can use someone's skill in one to infer their skill in the other, which is a good rule of thumb for evaluating potential teachers and spiritual friends.