Want suggestions on choosing open source embedded BI tool
You can try Power BI - it can do all mentioned stuff ( and even more, you can plug in R/python code), but its not open-sourced, though you can go for a free 1-user account. 

I guess tableau can do the same and also has "community" version, but im a fan of Power BI, so cant tell more about it.

If you need some custom, build-from-scratch solution, you can go for Shiny - fully build on R, fully open sourced and has free hosting option, can be embedded as an iframe ( will prolly look horrible), but fully customizable and can be tuned the way you want it to be.

Similar to Shiny, but with Python: Dash