Hello, zideth
Welcome to Microsoft Community.
1. How are the data on the application and the data on the web synchronized?
Most of the time, Office automatically syncs changes to Office files saved in OneDrive. On rare occasions, if an Office app closes unexpectedly, or if changes made from different devices can't be resolved, a sync conflict can occur. If you run into problems with changes not syncing or merging properly, you might want to change your sync settings in OneDrive. See more details in Use Office applications to sync Office files that I open (microsoft.com)
2. How to update the data on the Excel worksheets as soon as the author updates?
You and your colleagues can open and work on the same Excel workbook. This is called co-authoring. When you co-author, you can see each other's changes quickly—in a matter of seconds. And with certain versions of Excel, you'll see other people's selections in different colors. If you're using a version of Excel that supports co-authoring, you can select Share in the upper-right corner, type email addresses, and then choose a cloud location. But if you need more details, like which versions are supported and where the file can be stored, this article will walk you through the process. See more details in Collaborate on Excel workbooks at the same time with co-authoring (microsoft.com)
3. Why is this notice being displayed to me as a viewer only?
When someone shares a file in OneDrive, they can choose whether other people can edit, can review or can only view the file. So it's possible that this person only gave you permission to view the file when they shared it with you in the first place. You can check with this person to see if this is the case. See more details in Share OneDrive files and folders (microsoft.com)
In addition, I'd like to know whether this is the only Excel document that has this issue, or it happens to other ones as well. This helps to determine where the problem lies.
Feel free to reply if you have other concerns.
Best regards,
Yuhao Li| Microsoft Community Support Specialist