Absolutely. You will get the most out of XcodeGen by adding your project to your .gitignore, as this way you avoid merge conflicts. But you can also check it in as a halfway step.
Note that you can run
xcodegenas a step in your build process on CI.
If files were added or removed in the new checkout you will most likely need to run xcodegen again so that your project will reference all your files. Unfortunately this is a manual step at the moment, but in the future this could be automated.
For now you can always add xcodegen as a git post-checkout hook.
Yes, simply generate your project and then run pod install which will integrate with your project and create a workspace.
At the moment there are no special options for code signing in XcodeGen, and this must be configured via regular build settings. For code signing to work, you need to tell Xcode which development team to use. This requires setting the DEVELOPMENT_TEAM and possibly CODE_SIGN_STYLE build settings. See Configuring build settings for how to do that