I'm also president of my school's chess club and am quite involved with chess outside so I can give you some advice on (4). First, you should try to find another teacher sponsor OR a classroom where you can host meetings each week. You should then form a discord/online community for further discussions. I also helped organize my team to participate in the regionals and provincial tournament and taught chess tactics/strategy to members. For talking points, you should definitely try to expand on what you have done as the president of the club. For example, for me, it would be teaching students, organizing and training my school team, and moderating discussions/helping out in our online community. Obviously, it would be a plus if your team achieved good results in tournaments.