Is there a Rules Condition for 'is user:' or 'is root user'? I am creating a rule that will help to manage permissions, but I only want it to run for the user with uid=1.

Is there a way to add a Rules Condition based on user data? Is such a condition prone to problems, and should I instead need to create a new permission?
Sure there is such Rules Condition. As an example, have a look at the Rule I included in my answer to "How to stop a Views block from displaying to admins, such as user/1?".

The Rules Condition included that answer performs a Data Comparison to check if the value of site:current-user:uid is not equal to 1 (in your case you'd want to check if it is equal to 1).

Note: This specific Rules Condition comes in handy for anything you want to enforce (or prohibit?) for super user user/1 (which typically skips all permissions), similar to what the question was about in the linked question here.