Is there a way I can link my Twitch to the site so I can stream my first speedrun and have it uploaded/validated as soon as it ends?

This website does not host any videos, all videos are hosted on other sites like YouTube or Twitch and are simply embedded via links/URLs.

So, no, you cannot do that, this site doesn't not support that nor will it probably ever support that (because how would it know when to download a run from any other stream).

Okay, understood.