How much do you consider a fair price for a chess coach (depending on his/her level, teaching skills, experience, fame, etc.)?

Hand down. Give a number (or a close range).

IMPORTANT Just not saying a number (X or Y-Z, in your local currency), but add more context, that is chess knowledge level, teaching skills, fame "I saw him/her on social media/at this important tournament", other elements.

1. How much does it varies depending of "external" factor like 1-1 / class lessons, remove / in person lectures?

Coaching is a work, so it must be paid (otherwise it would be volunteering, community service).

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2. If you are yourself a coach, share your experience (whether you are amateur, doing it as second job/extra gig, or a full-time titled player doing it as a career)?

3. How do you get there? Do you fear competitors?

I have a coach (1-1 in person lessons) and I'm completely satisfied by him. Money wise, I cannot say if he charges me a fair price (I tried to find rates of similar coaches on lichess (https://lichess.org/coach) but most of them have the message "contact me". so little-to-zero data available).

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I have an extra question.

4. As a chess worker (professional) are you a "full time teacher" only (beyond playing yourself in some competitive tournaments) or you do extra supplemental activities (I read that very few people "just teach", but do "teach + extra stuff)?

TIA