ground

Thoughts can indirectly affect matter, i.e. the appearance of matter, which is obvious in the sphere of science.

"Perception" is common parlance and as such it isn't an illusion but a conventional linguistic expression valid in certain contexts. In spiritual traditions the term "illusion" in the context of perception is applied for phenomena perceived since they are said to appear in a way which does not corrrespond to their ultimate mode of existence.

what qualifies a "master"?

your questions which appear strange in the context of conventional "every-day life" evoke the following question: what meaning does the expression "I know" have for you? i.e. when would you feel entitled to say "I know {this or that}"? what meaning do the expressions "exist" and "existence" have for? Asking "is it real?" evokes the question: what meaning do the expressions "real" and "reality" have for? The funny thing is that your questions are based on the hypotheses that "existence" and "reality" are more than mere baseless ideas. But how can you "know" ?

Calming the mind, being able to concentrate and think logically, experience the relativity of perception ... these are my ideas as to benefits.

Of course since every type of logic is a convention in the first place and if one does not agree to a convention of logic one cannot apply any logic at all. In some contexts however one will not be able to succeed at all if one does not apply a conventional logic, e.g. if one works in science.

The fact that "responsibility" is a thought before it is being expressed linguistically through speech or writing does not negate that it is an individual's decision to letting him-/herself being guided by the thought "my responsibility" or not. you can reject your responsibility or accept it. It is completely up to you, i.e. it is your decision, but from that you should not conclude that others will share or accept your view.

I'd suggest to look there for the start: https://en.wikipedia.org/wiki/Logic

There is a difference between being able to choose one's thoughts and letting oneself being guided by them. The latter lies in the sphere of an individual's responsibility