"Here are the cats."
Because вот means "here is" (when you're presenting/announcing something) and здесь/тут means that something/someone is here.
The english phrase can be taken either way tho, "here are the cats" like they're being presented or "here are the cats" like here they are I found them.
Is коты more formal like "cats" and кошки more like "kitties" (diminutive, informal, familiar)?
Кот is specifically a tomcat. Коты would only be used when you know that all the cats are male. Кошка/кошки is what you use generally, when the gender of the cat(s) is unknown, irrelevant, mixed or they are female.
I dont understand why it wouldnt be вот ето кошки instead of вот и кошки which theyre saying
It doesn't make sense in english because of the phrase. It makes sense in Russian. It would translate more like... if someone wanted to see the cats and you took them over and presented "and here are the cats (that we were talking about)." However this absolutely isn't the most direct translation and should be used in such an early stage of learning without context.