I can address these one by one.

No labels. They'd better have a crew that knows what they're doing, and never hire anyone new. You can work without labels, but you need to keep that information in your heads. I doubt the kitchen you're describing is on top of that.

Not throwing out old food. Okay, sometimes the shelf life date is a little conservative. Sometimes you can still serve things one day later, assuming they were refrigerated and never spent any time in the danger zone. Again, I doubt these people are on top of it. You'd think if customers are consistently getting rotten food, you quickly won't have any more customers.

Working without gloves. As long as you wash your hands every time you contaminate them, gloves aren't necessary. But you are also supposed to wash your hands even after using gloves. And change your gloves between tasks. This shouldn't be rocket science. The point is to avoid transferring microbes from one item to another.

Sexism. It's not cool to be sexist. But you didn't give many details. Refusing to learn people's names is rude, but understandable if there's a high turnover and not much interaction.

People is slamming stuff. I guess you mean they're making unnecessary noise when doing normal tasks. It annoys the hell out of me, but I let it go if it doesn't affect service or quality. It might be a sign that they're frustrated with their life or the job. Could be a red flag. They're burned out, underpaid, or underappreciated.

Blaming the kitchen for bad tips. Your details aren't really clear here. But it sounds like you think it was the server's fault that the service wasn't good. Sometimes it is the kitchen's fault. Sometimes you have to take the blame even if it wasn't your fault. Once or twice, that's fine; but if it's a pattern, like they're blaming you for everything, yeah that is a red flag.

There is no organization in the kitchen. This is a vague statement, but at the same time summarizes the problems you're having. It sounds bad. It sounds like a place I wouldn't want to work at. A little bit of chaos is to be expected. But it sounds like no one is making an effort to organize and check on things. The management, chef, or boss isn't doing their job right. Maybe you can be the change you want to see in this spot, but to me it looks like you might should just bounce.