I finished downloading a pruned version of Bitcoin Core. I see the network traffic moving, does this mean I am actually running a node?
Yes.
Is there more I should do next?
I saw a video that showed a guy allowing incoming connections on bitnodes.io.
That video probably used bitnodes.io to verify his node actually can accept incoming connection.
Also, I noticed I'm using client version 27.0 is that correct?
It's not latest version of Bitcoin Core, but you won't face problem running older version.
When Bitcoin gets updated does it require one to reinstall Bitcoin Core?
What do you mean by update? If you mean network upgrade (such as SegWit addition), you're not required to upgrade version of Bitcoin Core. But you'll miss feature and functionality related with the network update.
Just like 28.0, when it moves on to 29.0 etc. But one responded that it isn't a problem to use an older version. Thanks for everyone's responses.