Use fastapi with AWS websocket api gateway

Question

I have a FastAPI working on an EC2 under REST api with some endpoints. Now I would like to use it under a websocket api. To do this I have a few questions:

1. On my FastAPI, what shoud I do? I have read they introduce mangnum and a handler main for magnum, but they always have only one endpoint and I have several endpoints.
2. Also, they always use a lambda function. Could I use an EC2?
3. How do $connection and $disconnection work in this case? What do I have to introduce in my fastapi so I can still use my endpoints?

Processes inside my fastapi can take long to answer (eg. 20s). Therefore, I need to move to websocket to avoid timeouts. If you think I can have a better solution in a different way I'll happy to know about it.