Hello again,
on your first question: TLC will indeed stop at the first error, so you probably want to perform the reachability check separately from verifying other invariants.
About the second item, I can only encourage you to document your specifications, including the properties that are checked. In a CI context, you can indicate which outcome is considered an error. For checking reachability, you want to invert the standard interpretation and consider "successful verification" an error.
Regards,