Where is Jenkins Pipeline script stored and can I control it?
The good news, is that you absolutely don't have to use that little box to manage your pipeline script.
Jenkins also allows you to source your Jenkinsfile from an SCM repository like GitHub, and will even let you automagically import branches as separate jobs with separate Jenkinsfiles per branch using multibranch pipelines.
Pipeline scripts are in a language known as Groovy, not Perl or sh or similar. The definitive guides to Groovy are (of course) the Jenkins reference guide and the Groovy reference guide.