Couple of questions here.
Here are what I know.
1. Common Data Service is first introduced together with PowerApps, Microsoft Flow, aims to build Apps using PowerApps seamlessly. And now it adds a new feature call Data Integration with Dynamics 365, which would be more powerful when deal with enterprise data, and the corresponding scenarios. You may start from here : Common Data Service.
For Data import or Export, see: Import or export data from the Common Data Service
2. CDS doesn't open its API for public access currently, but you could access it through CDS SDK, take a look at the response from staff pvillads on 08-02-2017 05:11 PM:
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We have an API that can be used to access the data in the Common Data Service. This SDK works by creating a document that is then sent as JSON file to a REST endpoint for execution. However, we do not publish that endpoint at this time. You can always create a web api that accepts your document, and then uses the CDS SDK to get the data and then send back the results, so two hops instead of one.
I believe that is the best you can do for now. Let us know if you wish to partake in the private preview of the CDS SDK.
BR PV
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To answer your second question, you may take a look at the CDS SDK, to see if the 3rd BI tools could work with the CDS API.
3. For the third question, if you mean Server side logs, no, currently auditing is not available.We have feedbacks submitted on this part already. For Microsoft Flow, there is a blog talking about how to export Flow activities, check:
Accessing Office 365 Security & Compliance Center logs from Microsoft Flow
Besides, for Approval part, if here you are using Microsoft Flow, and as recommended by Meneghino, it is much better to keep a table to record the history, and update the table per Approval status. Adding Flow blog for reference: Error handling process
4. Check the Approval part in Microsoft Flow:
Creating Approvals

You could simply switch the Approver in the Approval Action.
For delegation part, if the Approval is not executed after a range of time, then we could configure a timeout action to forward the Approval to another person. (Refer Error handling process ).
Hope the information above is helpful.
Regards,
Michael