Nobody expects or wants you to show up in a suit and tie if it's 80 degrees out and the AC is broken, but very few people object to you dressing up more than required. Dress at least as formally as you expect your interviewer to be, if he's wearing a polo shirt, you can too, but a shirt and tie is better, and if you don't like the cut of your suit jacket, you can drape it over your shoulder. But the default is white full-sleeve with a tie and that's usually best.

Leadership questions, depending on who asks them, tend to be either rote questions expecting rote answer or are from someone who does hold a leadership position and will get glaze eyed if you give a platitude. I'd wrap my answer to strength/weakness into my answer on leadership, if I were you, or vice versa, depending on which gets asked first, e.g.

"What is leadership?"

"I think that depends on three factors. Who's leading, who's being led, and what the situation is. As a leader, you have to use a style of leadership that's compatible with you, and you need to have a number of methods, not just one, so you can use one that works for you and that works well on the person you're leading. I think that's my biggest strength, adaptability. I know I can change my approach to be appropriate to the person and situation. What works on John, to keep him motivated and enthusiastic, might not work well on Jane. Jane might be best suited with a supervisor that makes it clear that she is trusted to do her job, and worries if you come by checking up on her too much, but John might - and I think this is true of lots of new employees - get worried if I don't come by checking up regularly. He gets worried and he doesn't know what to do if he has free hands for a bit, so he needs direction. Whereas Jane merely needs to know that you trust her to be assigned a task and figure out how to get it done. So you have to be adaptable in your leadership style and I think that's one of my strong points. A lot of times though, your strengths are coupled to your weaknesses. Part of being adaptable in leadership style, especially when your younger and don't have dozens or hundreds of prior examples to draw methods from, is that you have to get to know your employees. So you have to worry about becoming friends and not just friendly, you also have to worry about others perceiving that to be the case. You might know that your not close friends with John, just have a friendly work relationship, but Jane and Tim might not see it that way, and maybe John doesn't either, and you have to be careful about that. I think of myself as a friendly person and in a supervisor, that can be a weakness if you're not careful. So you have to keep your ear to the ground and when possible draw from the greater experience of your fellow supervisors and your own boss, they'll often be in a good position to warn you before something becomes a problem."

Typically that method to answering questions, even one's that haven't been asked, will do you better than trying for rote answers. But asking and answering them yourself before they are asked, it allows you give a genuine response - and that's important - while essentially controlling the answer. The interviewer knows your answer now, and having already explained your reasoning, even if they ask again, you can give a thinner answer without it seeming that way. So if he asks again, strength/weakness, you can just say "Well, I'd stay with adaptable" and then weakness "I guess the short answer is I might be too personable, or might be perceived that way." Now, what you've actually done there, since your interviewer is a supervisor themself, is likely summoned several prior personal memories to mind, like when one of their employees complained they showed favoritism etc, and their own context will almost definitely fill in the blank for you in a positive fashion, essentially a "I know how that goes" in their head.

Otherwise, come off confident - that's where genuine answers help, people get nervous giving rote answers and such - dress one step above standard, don't be overly-familiar, even if it's someone you know a "sir" rarely hurts, if they stop you on that you can always just say. "Sorry, I'm a little nervous, I've been worried about whether or not I'll be respected as a supervisor and its made me think maybe I've not always showed the right amount of deference, you can't expect people to respect their supervisor if that person doesn't show they respect their own supervisor." Really you just have to be fast on your feet and that's where genuine responses help, along with preparation, because it let's you respond faster.