I would assume their entrances existed before the Muggles did in the area. They were just adapted to the times.

Why keep things grouped together when you have magic. There's no point.

 

You mean one entrance is through the phone booth and the barrier, respectively.

For the Ministry we know that there are floos, and I see no reason why there shouldn't be floos at platform 9-3/4, other than the fact that they aren't mentioned. Plus, I presume you can apparate there. If you're asking for the reason those entrances (also the Leaky Cauldron Charing Cross entry) exist, I presume it's a backup for Muggleborns, mostly. It's unfortunate that Harry is basically a Muggleborn in this regard; we get a warped perspective. It's entirely possible (even plausible, given their ignorance) that the average wizard goes about their life, including travelling, without ever even seeing a Muggle.

If that's true, it doesn't really get any more separate.

 

Well, possibly. I would only raise that (i) I see no reason why the Ministry couldn't install floos there, so it makes no sense to have none, and (ii) the Weasleys go through the barrier for plot reasons in PS, because Harry needs to encounter them.

The latter naturally means that if asked, Rowling could make up any arbitrary reason why connecting platform 9-3/4 with floos does not work, and neither apparating there, and that would be that, but from a structural point of view, to behave as the rest of the wizarding world does, you'd expect ways to travel there, without moving through the Muggle world -- precisely because they are so separate.