Hey Coach,
Welcome to the site. I know you posted a few times a few weeks ago about some interview questions and didn't get answers. I think, similar to these questions, the ones asked were particularly specific to your school and your personal background and experiences so it is difficult for myself and others to comment.
Based on some of your previous questions, it sounds like the current baseball program has a bit of a bad culture and not a great relationship with the booster club. So, administration is likely looking for some assurances that whoever they bring in can work toward improving both issues. Therefore you would need to have some understanding of the situation as well as a plan and ability to execute the plan.
I don't know your background, strengths and weaknesses or extent of knowledge of the specific school circumstances so I can't address many of the questions but there seems to be a need for sensitivity to these issues. So anything you can communicate to them that suggests you can relate to the issues and execute a plan to improve them would be advisable. If you don't know exactly what the issues are but have experience working through athletics/boosters issues and/or finding creative ways to motivate a historically unmotivated group, those things would be worth stating. Most administration groups charged with hiring coaches want to hear that those coaches will do their best to work within the often-limited parameters that school districts must operate under.
For your weaknesses, it is always a good idea to tie into a related strength. For example, "I was an OF in college, so I am much more able to drill down to detail levels of instruction with fielding and hitting than pitching so I guess teaching pitching is a relative weakness".
For accomplishments, you probably want to put more emphasis on how you may have motivated a group toward success as opposed to focus on your individual playing accomplishments.
For coach role with booster club, the likely best answer is that you understand your role is to learn how the booster club operates and work within their guidelines to best support your program.
In general, keep in mind that things like safety and compliance are often higher on the priority list for administration than coach playing experience or ability to win.
I'll be honest... some of your questions leave me wondering if you have the experience or background that is ready to jump into such a situation. Would you mind sharing more about the program (not the name) and how you see yourself fitting in?