1. PUGs are a great opportunity to practice personal aspects of your play (DM, general positioning, other classes) but scrims will always be the better option if you want to improve 'across the board'. Nothing beats practicing 6s than playing 6s properly.
2. A good mentor is one that helps you grow, not someone who is a walking encyclopedia of knowledge. Any invite/prem player could give you tips, but a mentor that works on your own playstyle and you as a person is infinitely more valuable. Certainly, a mentor with extensive knowledge on the game is important. However, if you are struggling with the non-game elements (communicating properly, working with your team, avoiding tilt) that is going to be a major roadblock to your success as you progress.
3. A player is only as good as their team, and vice versa. If there is an issue within your team (e.g. your flank dies very early in teamfights or your med drops a lot) that's a conversation your team needs to have. Thinking in terms of "X is holding us back" or "I'm holding them back" is the wrong way to approach that problem.
4. A lot of well performing teams are ones that have stuck together for a long time, or at least have a good portion of the team who have. This is because you become friends with one another, communicate more naturally and develop in-game dynamics with one another. If each individual splits and tries to find teams, more often than not you'll be joining a team of complete strangers or being new in an existing team. In either case you have to get to know one another before you can learn to play with each other, which takes more than one season.
5. Whichever mode of practice you pick (DM, MGE, Offline, Jump), whats important is what you get out of it. Theres a term in psychology known as Deliberate Practice. In simple terms, it refers to a structured approach to practice that focuses on identifying areas of improvement and developing sessions to develop that specific area. In terms of TF2, you could, for example, find that your Scout vs Soldier is pretty poor. To improve this, you spend the next couple of weeks before scrims doing some Scout/Solly MGE to warm up and figure out where you can get better. There is no BEST way to improve DM or Movement, but determining your weak points and focusing on that will make improving feel more natural.
6. Just through spectating, Invite Players appear to make correct choices more often. In actuality its hours upon hours of practice and years of experience. Main Players seem to make more mistakes, which is to be expected.
7. Pretty much what carter said.
8. Improving comms, much like anything, takes practice. But generally speaking good comms do one key thing, they let people know about something they do not currently know but should. The odd spam rocket is not worth calling, but that spam rocket hitting 4 people probably is, for example. Determining what you as an individual should say and how your team as a whole communicates is just something you need to figure out with your team, it all depends on how they work.
9. Natural talent is definitely a thing, but the cases in which things just 'click' for an individual is incredibly rare. Practice and mentality is a much bigger contributor than raw talent.
10. Soldier goes zoom, airshots make brain feel good.