Why does one repository make two tables?
Because an issue and a pull request are different things, and almost every question you would ask is about one or the other. Review duration is a pull request question; time to fix is an issue question. Putting them in one table would mean every filter starting by separating them again, and a rollup that counted both would answer something nobody asked.
Do comments come across?
No, and the import reports that rather than leaving you to notice. Issue and pull request records only; the discussion threads and review comments stay in GitHub. That is deliberate — the conversation is where engineers work, and copying it produces two half-threads. What comes across is the state everybody else needs: who, what, when, and whether it is done.
I can only see my personal repositories. Why?
Organisation repositories need the organisation permission granted at sign-in, and some organisations additionally require an administrator to approve third-party access before anything owned by them is visible. Without it the import genuinely finds nothing under the organisation, which reads as an empty account rather than as a permission that was never granted.
Why does it ask for such broad repository access?
Because GitHub's classic OAuth scopes are coarse: the only one that can read issues on a private repository also grants write. The narrower alternative covers public repositories only, which would break the feature for anybody whose work is private. It is the least-privilege option available for the job rather than a convenience, and nothing in the connector writes to a repository beyond opening an issue you asked it to.
Does the table keep up with the repository?
It can, an hour behind at best. Importing again updates both tables, matched on the issue or pull request number, and Keep in sync does that hourly or daily; nothing is written back to GitHub by it. Each run reads the 2,000 most recently updated issues and the same number of pull requests, so on a busy repository an item left untouched long enough stops being refreshed, though it stays in the table. Anybody who needs the state to the minute should be looking at GitHub.