Thank you for taking the time to go into detail about this.
1. 3 times a week, 1 hour each week of coaching.
2. I recently started playing about 4 or 5 hours per week outside of coaching.
3. I didn't play much outside of coaching mostly because I couldn't find a group to play with. But my coach said a little over a month ago to wait a bit longer to improve basic technique before playing games. He's fine with it now.
4+5. I haven't asked about any broader issues or tactics/strategy. When I do ask about learning a specific technique, he will oblige.
6. Yes I do, and I spend time reviewing it after training. My coach generally identifies what my biggest technique issues are but sometimes I will make changes on my own (e.g. taking an initial step with my left foot before a step around is something I learned online).
7. There apparently aren't organized leagues and tournaments for beginner adults in my city in Vietnam. I intend on playing in the USA when I'm back visiting and have USATT membership.
Another thing to mention is that coaching is very inexpensive in Vietnam where I'm living. My coach charges $10 per hour. So maybe there will come a point where my development is stalled and I will pay for a more expensive coach like Ti Long who lives in my city.
Are you left handed?
It sounds like you are largely in a good situation. Better player doesn't necessarily mean better coach, especially for a specific player. It is more important as an adult learner go find good mentors who invest time in you and the fact you and your coach review your video is a good sign. Does he teach you how to return and read serves?
Most of the match play issues beginners have are tied to game reading skills. Usually a coach makes everything obvious and it is an opponents job to overload you and your job to overload the opponent. So an opponent may serve to you and you cant return the serve. This is actually a good thing for you though it might not feel that way at the time lol. Because when you learn to read and return the serve, you become a better player. But then quality of return becomes important as you need to be able to prevent the opponent from doing what they want.
Another thing that adult learners struggle to do is construct their game. You need to know what your approach is to winning points. Keeping the ball on the table is a basic strategy but it describes too many playing styles. You need to know what you intend to do to cause your opponent trouble. Some of this you learn by seeing what you do well, some of you learn by seeing what opponents struggle with. But a good coach will help you do what you do well to win matches and then balance out your weaknesses. There is too much to learn so having imbalanced play is normal for an adult. It just means you have to spend time patching weaknesses and improving strengths as you get better.
As an adult, you have to continue to seek challenges to improve and you can't leave it entirely with the coach though a coach can play a big role. In places like Vietnam (I am Nigerian), there might be a handicap/hustle system where good players play weaker players for money with a handicap in place to make it competitive. It is a good way to pay for unofficial coaching if one is can afford it as the better players will always try to hustle you (they can't beat you so badly that you never want to play but they also can't let you take the money) so you end up playing interestingly competitive points and get teased with chances to hit easy balls even if they know they can serve you off the table.
As you might have gleaned on the forum,some of the match play issues learners have are tied to how they view the improvement process. You should work towards being able to generate good spin and quality on your shots and ask your coach how you can do this within the technical framework he is teaching you. Hitting the ball properly with consistency, placement, speed and spin is as important if not more important than moving well, the solution is to find better players to play against or more challenging serves or exercises to execute whenever one wants to improve rather than being stuck repeating the same things forever. The good thing about the USATT rating system is that it makes it easier to measure your level and what kinds of opponents might be competitive for you. So you have ways to measure improvement. It can have negative side effects as well, but that is life.
The challenges will force you to evolve and then you have add things to your game to get better. It is easy to fool yourself that what you are doing is 100% adequate in the absence of appropriate challenges so let the challenges determine that.