3. Rasperry Pi's have pretty limited specs all round. The user experience is going to depend entirely on how complex your dashboard is, so it's going to vary based on the use case.
4. Online or Server won't really make a difference to the Raspberry Pi. The HTML being returned by server / online will be treated in the same way. Where this would make a difference though is how big you'd build out your server. If you have unlimited budget, you're probably going to be able to get better performance than you would on Tableau Online. If you have a small budget and can only afford a tiny server, it will probably perform worse than Tableau Online.
The location of your data is important as well. Tableau Online can reach onpremise data - if you're using a live connection though, i'd expect it to be slower than a live connection between Tableau Server and your database server on the same network. If you're using extracted data, then it's not really applicable.