@Ivan G. As of right now, the default browser for Synthetics is google Chrome. There is currently no feature that will allow you to launch synthetics via IE. Maybe on the roadmap for a future release. I would recommend putting in a Request Feature Enhancement (RFE)
You can create a RFE from the following Link: https://answers.dynatrace.com/content/idea/post.html
Please note, it is important to select the location as "Product Ideas" as this is where the PM's go to select features for their roadmap.
You do not need the plugin on the server. If you want to record synthetic click paths the plugin is required on your Company laptop/Desktop that is used to work within the Dynatrace UI.
@Ivan G. I'm going to say that the technology that is serving up your video is either outdated and/or unsupported. My reasoning is that I am able to hit youtube videos with my synthetic monitor with no issues, as well as interact with the page. I would recommend opening a support ticket where a Dynatrace Support rep can dive deeper into this issue.
Being that I am not able to access your environment and take a look at the issue, I would recommend reaching out to Dynatrace support by creating a support ticket. Or, if you are a dynatrace One customer, you can reach out to support via the chat.