If I upload Contacts via the Ringotel shell for an organization and a user edits the contact via the ringotel app. Does it update contact shared between all users.

Details of the contacts that an admin added cannot be edited by users. But users can add additional details to those contacts that would be visible to all other users. For example, they can add an additional phone number or add some notes - anything that an admin hasn't added.

With integrations, everything works depending on the service. With Google, every user uses their personal authentication to access their contacts. All contacts get synchronized with their contacts lists depending on Google contact settings. As far as I know, a Google Suite admin can make some contacts accessible for multiple users