No, but since Element led by some of the same people as Matrix, I want to observe the type of open core project it is. Is it more like GitLab or more like Supabase? GitLab has a lot of help for self-hosting, while with Supabase if you want to run its components on your own it's up to you.
Unlike GitLab, Matrix is not open core, and so isn't Element or Synapse, they properly and fully open source.
Also, Element is just some JavaScript in your browser or electron shell, there's no need to self-host it really, although you can (just put some HTML+CSS+JS up on a webserver) — you want to self-host Synapse, and that's trivial to do (there's a Debian package, a Docker image and so on).
Scalar (the integration manager) is not open source [1] (though there was some effort to reverse-engineer its protocol [2]); and some of their anti-abuse scripts aren't public [3]
It sure seems to be. Look at the red X's and green checkmarks in the comparison: https://element.io/pricing There are different opinions on what Open Core means though.
Some of their bridges (e.g. Teams bridge) aren't open source. But those are separate software projects. AFAIK synapse and element aren't open core but fully open source (with apache licensing).