On systems Systems themselves won't solve problems for you or make your life easier. The best example is a calendar. Having a calendar with all of your tasks and events listed is a good thing for organization, but it doesn't inherently make your life easier. You could still horrible at scheduling things and forget to use the calendar. You could schedule too many things, and no calendar can solve the problem of your life being too hectic. Similarly, a task manager can't solve the problem of you failing to prioritize your tasks. It won't fix your lack of focus on the few tasks that actually matter. These are all systems, and it's not about which system you use, per se, it's about using the system correctly and making sure that it works. The saying goes that the best camera is the one you have on you. The best system is the one you use. If you want to use a different system, take the time to learn how to best use it and commit to using it. Always worry less about your systems and more about keeping your work clear and prioritized in your own head. This will solve many problems on its own.
On dual-monitors If you can't do the work on one monitor, you're probably not focused enough.
On habit When working with other people, be careful not to fall into their habits by way of exposure to them. Especially with mentors, it is easy to take their actions as a given and follow them accordingly. Their actions, simply because they are mentors and currently in a superior position than you, are not always correct. Don't begin to adopt their way of doing things without being aware of it. The easiest habits of theirs to adopt unconsciously are their bad ones. Their vices. Their bad temperament. Since you are exposed to a mentor so much, you'll begin to see the pitfalls that you didn't see beforehand because you were never so close to them. Be mindful of these.
On observation In your early days of an apprenticeship or at a new job, spend all of your time observing and doing. Don't rush into making contributions, because you are not yet ready to. You don't have the requisite knowledge to understand the depths of what's going on around you. Don't act like you do. Take your time and observe the interactions between people in the organization. Observe how others do the work and how their superiors react to that. Figure out the group dynamics and general expectations. Slowly build awareness of how you should adjust your behavior to fit this environment. If you skip the initial step of observation, you will make too many mistakes to be effective. You won't understand your boundaries, and your efforts will fall short of the expectations of the group. You won't know what makes certain people happy or unhappy, and your efforts to do good work for them will fall dramatically short because of it.