Some pretty basic questions;
1 - can PowerBI be used as complete stand-alone on premise solution without using any Cloud services ?
2 - if used completely on premise, will be any downsides or limitations?
3 - if used on premise, can reports be published to the web on a local intranet, for example ?
4 - performance of the REST api: I've not seen any data on performance of transferring large volumes of data into PowerBI datasets using the REST API - are there any metrics out there?
5 - If using the REST API for adding rows to a table, is there any guidance for what provided best performance, e.g. 1 row at a time, 100/250/500/all rows at a time ?
No. Power BI can't be used as a completely stand-alone on premise solution. Even you use SSRS 2016 report server to integrate Power BI, you still need to interact with the AAD. See: Power BI Report Server Integration (Configuration Manager). So when you get offline completely, you can only access the .pbix created in Power BI Desktop.
For the REST API, there's no "best practice" guide for performance. Just pay attention to: Power BI REST API limitations
If I rephrase my question better - can your data be kept on premise and and not moved to the cloud? So for example, can the REST api be used to populate datasets locally, although authentication etc. may need to happen on-line?
as far as i know,no there is no way to push datasets in PowerBI desktop, but you can always refresh or use Direct query,
I think you may get more answers if you say exactly what you want to do.
bottom line, if you want something like PowerBI on premise you have to wait for SQL server Vnext