Not really, you lose the remote app on your phone, which is useful to enter passwords, but using the voice dictation to enter a password a character at a time works surprisingly well.
You'd also not have airplay and mirroring. That might be a bigger deal for some, but for me, it's a feature I basically never use.
The YouTube apps on Android and iOS support streaming to the Apple TV YouTube app, which seems to be the bulk of what my guests and I want to actually stream. If you have a local media library, or tend to want to stream your computer screen to your TV for unsupported media/sources (or for plain mirroring), lack of AirPlay might be more important to you.
If it’s like the older Apple TV’s no. It comes with its own remote, the only iPhone integration is that your phone becomes an extra remote should the original be lost or broken
No, Apple TV doesn't require any other Apple devices. It will prompt you for an iCloud account during setup, but you can create a free one or just not have one.
I guess you would not be able to stream your display to the Apple TV, and you would not be able to use your phone for keyboard input, and probably more. Just get an iPhone already!