inflex

Fundamental. I believe in coaching, in itself as a tool to redesign one's play at the microscopic level. It is also adaptive, to a certain degree.
To develop a strong player, means to make sure the fundamentals and core basis are on point. It means to adapt to the students personality and their level of commitment. Since I can coach for that matter, someone that is a Platinum level player and plays mostly for fun, but wants to get tiny bit better at what they do to perform a little more while playing with friends - and there is nothing inherently wrong with that - it is a video game after all ; We can surely take a player that is in it for a long run - want to improve fundamentally and become a strong player with big goals in mind. I can also coach an individual that is opting high up - to become a high elo, that brings in a lot of value and knowledge with his own presence. Latter, obviously requires a lot of work, therefore I'm demanding much more at this stage, in commitment.

Meta is a term that applies in two worlds of League of Legends. Soloq/ranked environment as well as competitive play. We shall bear in mind, that strictly speaking these are two different games.
When it comes to meta for majority of the player base it wouldn't matter too much. If a player learns the fundamentals and stick to his own champion pool, within his own goal of getting better - most of the time it won't struck him of what is popular, or meta at the time. Of course, changes do happen and champions get changed. Map gets changed, items are different and the overall balance is rather at a satisfactory level, however CORE LEAGUE OF LEGENDS almost never change. Past these years, the core game is very much the same. Only and most recent change that involves game mechanics are the side lanes catching up faster with the center (mid) that changes dynamics a bit.
I myself play soloq from time to time and watch the KR & Chinese soloq streams as well as some VODs. Data is important too.

No, I do not boost ranks. Riot Games strictly forbids these activities and for a good reason. Rank itself, always was and will be tempting to be tempered with by hiring third parties. However, I am strongly against this.

It depends on the individual that I'm coaching. His own commitment level, behavior, personality as well as skills that he had engraved in himself over the years. Habits that are to replenish, and ones that are to be replaced.
I. Fundamental way of looking at what the learning process really is.
II. How to learn and practice.
III. Champion pool - what champions help you learn the game and what champions should we stay away from?
IV. How to get on track for the long run.
V. Watching VODs and gathering data.
Of course, coaching is broken down to many different parts, learning what soloq really is and how we can impact it while learning is no easy task. Complexity of the game itself, can quickly overwhelm us. If we look at any other game or sports, there are some baseline skills that we could outline and train individually - but not in League of Legends. Creating isolated environment is difficult as well, since there are no available tools other than playing and grinding.

Again, it heavily depends. I won't go in details of waves core mechanics if a player doesn't even know how to punish opponent that had locked himself in the auto-attack animation. We probably will never talk about that one Baron fight that with the same setup most likely will not happen again (things where we have to look at X1, X2, X3, X4, "player, Y1, Y2, Y3, Y4, Y5 where X is allies and Y is opponents; looking at all the levels and/or items factors; mana; cooldowns; wave states; game state; etc.) and definitely we shouldn't opt into this if one's laning phase is far from perfect.
Most important thing in gameplay analysis is the coaches ability to select, focus and outline parts that actually matter for the coachee (student).

This has already been answered in the previous questions.
To add up: team's objectives rarely exist in a soloq game. Player should focus on repetitive parts that can be improved upon (especially in the lower elo part of the community) and driving up to deliver the game as quickly as possible. Otherwise we run into numerous complications - longer the game goes.
If one can understand, that soloq can be sensed as a single player game - where we cannot control 'our NPCs' (teammates we meet playing soloq) and he's able to progress himself in this whole story of grinding countless league games, the sooner he will start seeing results.

Typical coaching session consists of an introduction, interview with the player and - yet again - depending on their expertise (simply put: elo) we will talk through few topics regarding soloq and learning the game itself. Live game+VOD review is a standard format that can be modified according to the needs of the coachee and/or any technical inconveniences.
Team coaching is a completely different process that usually involves a lot more time and work, that is optimized with the manager first. If we are talking about amateur teams, usually they ask for a VOD review with them on call.

I think it's impossible to answer this question within a 1000 characters mark. Team Coaching is a topic far more advanced. Specifically when we are looking at semi-professional and/or college/academy teams. It usually involves team's manager, captain and often times either a second person that helps me with data and planning out the session or their backup.
Building a successful team start with picking right players, usually individuals that do not need 20+ hours of individual coaching with them as that undercuts both budget, and the given time. Besides the league and the game knowledge itself, there are many aspects such as communication, discipline and the willingness to improve that come together at the high level competition that must be in place. Otherwise the team is shattered.

Simply put, it is a Discord call, so the communication channel is rather simple.
For the communication to be effective however, there are more things that come to play the pivot role.
Feedback is most often provided with the VOD review (that I have recorded from their POV) right after the session but the follow ups and the docs as a sort of material are always available. Most student stay in touch with me, and I'm open for discussion and questions they might have.

There's been a bunch of players that had reached higher elos that they ever had expected out of them.
There were individuals that were able to climb from Silver to Master in a single season. Some teams have gotten into their academy/college playoffs, other were able to secure playoffs at the Prime League.
Regardless, one of the most important gigs I have secured and success that I've had, was when I was coaching a Swedish Team of amateurs. I was able to not only improve their gameplay, but most importantly their enjoyment from playing the game with each other. I have played with them from time to time and I'm happy to find out they still play Clash together. As it comes, one that I'm most proud of was the one where we've delivered the most fun possible - it was super positive experience.

I think it's hard to find a good coach. If you are Iron to Diamond player and you pay 10 bucks to the Master player to go over your gameplay you might learn absolutely nothing.
You might pay a Challenger streamer that is a really good player themselves a 100 bucks and still learn nothing. To go over the gameplay itself, can be done by a lot of players that are bit more higher ranked than majority of the player base.
However, to actually learn about the game and make sure the processes are understood it takes someone that know how to coach and guide someone. As opposed to showing them X and Y - telling them to do this and that. That doesn't help. It really, rarely accomplishes anything. I hope someone is able to look at the interviews here and find someone that fits what they expect!