I think the important thing here is to pick your battles. Every kid in a two-family home situation is going to have different rules at their primary home as with their secondary. Personally, I would treat it as if she was at a sleepover with a friend, particularly since you're not sharing custody - this is a rare occurrence and makes it easy for you to treat it as a "treat" situation.
The other person is responsible for their general well being but shouldn't necessarily be expected to adhere to all of your standard chores and "maintenance". As such, things like TV time restrictions and bed times/wake up times aren't necessarily expected to be followed but you should talk with your daughter to be clear that she understand the difference between home time and this special time at her mother's house. Though, with maintenance tasks you should expect your daughter to manage these things herself to some degree.
At 7 she's more than capable of brushing teeth and hair on her own, provided that she has the necessary equipment. And, if she doesn't, that's a good time to talk about consequences.
- If her hair gets uncontrollably tangled if she doesn't brush it twice a day, then she will have to work more to brush it out when she forgets.
- If she doesn't brush her teeth, she could get cavities which will be painful and require going to the dentist to fix.
But take it at the level of seriousness it deserves - tangles can still be worked out, even with a couple of missed brushings and a day without tooth brushing isn't going to harm otherwise healthy and cared-for teeth. So long as your daughter understands that these aren't to become regular habits when at home, this isn't going to do much harm.
You say she wasn't given lunch... was she hungry? I've skipped lunch many times over my life, including as a kid, because I was so busy having fun and playing. As with missed teeth brushings, the occasional missed meals really aren't that big of a deal. Sometimes, if you ask a kid "What did you have for lunch yesterday?" and they say "nothing", it's important to ask the follow up "Why?". The same is true when discussing drinks. If she wasn't thirsty and didn't ask for water or milk or whatever beverage, then she's probably fine, particularly if it wasn't a very hot day likely to cause dehydration.
On the other side of things, if she was hungry and thirsty and asked for it, it's good to know why it was denied to her. Is your ex low-income? Is it possible that food was unavailable because they can't afford it? Even if this isn't the case, there's nothing wrong with packing a few snacks for your daughter to have if she gets hungry... heck, you could even send a few extra along to share. If confronted, you should be able to play it off as "they're her favorites and I wasn't sure if you had them".
One of the things you never mention in your question is what your daughter thought of the situation. You have a long list of things that are different from your home way of doing things but does that make them wrong? If your daughter had a good time and didn't cry to you that she never wants to see her mother again because it was awful, perhaps you're overthinking things. The goal is a happy, healthy kid and a day of excesses isn't going to harm either of those things.
This isn't to say that your list of grievances are all without concern. Some of the things on your list are important. Your daughter vomiting twice and not being cleaned up afterward (or encouraged to do so) seems important to me. If she vomited twice, that sounds like something that needs to be checked out unless she's prone to vomiting. Is she sick? Was there a clear explanation for the vomiting?
You're clearly concerned for your daughter, which is good but I think that expecting her time at her mother's to be identical to her time at home with you is going to drive you batty, hence my comment at the beginning to pick your battles. This will also help in your interaction with your ex. Instead of coming with a litany of wrongs, address the important ones and come to the interaction looking for information, not making accusations.
- Jane came home and said that she threw up twice last weekend - what happened? Was everything OK?
- Can I give you the contact info for her pediatrician in case something like this happens again?
- Would you please call me the next time it happens?