install – How to Check if Software is Installed with Homebrew

Take the path that you used for --prefix= during your ./configure and sym-link that into the Cellar/ directory that Homebrew is using. Homebrew will see these directories and see the dependencies as satisfied (unless you need to have them compiled with or without certain features to make Homebrew's formulas compile correctly). If your manually-compiled deps aren't compiled correctly, you'll probably get errors out of Homebrew.

ln -s /path/from/prefix/ /usr/local/Cellar/path/from/prefix

(Note the trailing slash on the first path, and lack of trailing slash on the second. OS X can be picky about these slashes when creating sym-links.)

This is the wrong way to do it, you should just be using --ignore-dependencies coq — that's what it's there for.

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.