If I delete the app, will I lose access to all my historic logs?
If you have created an account and are currently signed into that account : No logs will be lost. You can always sign in on a different device or web and your logs will be there.
If you haven't created an account or aren't signed into an account and you delete the app then you will loose access to any logs.
To check if you have an account go to “More” → “Account”