Merge two videos and send in api response

Both parts can be done using the LEADTOOLS multimedia toolkit. (Disclaimer: I am an employee of this library's vendor).

For the first part, the toolkit includes a demo that combines 2 videos, which is shown in this image:

 

Although this is a Windows Forms demo, the multimedia code inside it can be easily converted to server-side C# or VB.NET code that runs without a user interface (web application).
For the second part, there are different options for streaming depending on what type of computers or devices you want to stream to. These options are summarized in this page:
https://www.leadtools.com/sdk/multimedia/media-streaming-server