I'm not applying this cycle, but as someone who has done hundreds of interviews in her previous career, I'm pretty sure you're overanalyzing this to the point of sabatoging yourself. No one's going to reject your application because you wore a red tie.
Just pick something that matches and looks professional. Personally, I probably own about a dozen or so red suits. Can you guess what color I'm likely to wear to any interview I'm fortunate enough to schedule? It's a vibrant color and I like it. Plus, judging by this board alone, I'll probably be the only one there in red.
In my old profession, when they offered lunch on interview days, it wasn't really there for you to pig out. I'm guessing this is the same. As Lizzy M said, limit what you eat. Try something like pasta salad without a lot of dressing. If you have a sandwich, make sure it isn't loose meat that's likely to spill out onto your lap. Choose something like ham or turkey without shredded lettuce. Try not to get mustard, ketchup, or mayo. Or if you do, just get a little bit and make sure that you put a napkin on your lap. Don't put a tomato on it or pickles on it. If you have to have them, put them in your plate and eat them with your fork, unless you're eating with a group of people other than other interviewees because they may think that's a little weird. Drink water, Sprite, or 7-Up instead of Coke. If you do spill something, try to get it out immediately before it stains. Also, on white shirts if you have no choice and it's a SMALL stain, white-out works wonders.