Homebrew warning: "No developer tools installed" even though Xcode is installed
Yes, it is perfectly normal for homebrew to prompt you to install Xcode. That happened to me right after I installed Mavericks.

As for your question about git, it depends a lot on your usage. Default git (and almost every other tools) are not of the latest version. If you're OK with that, then of course you can just use the default one.