I would like to learn more about Webhooks and whether or not it is possible to create a note in Pipedrive that can then be saved on a different website that also has a “notes” area.
Webhooks will send request in a specific format that contains information about what changed in a particular entity (Note is one of them). Documentation about this format is described in detail in our Guide for Webhooks.
If your website has a public endpoint that can read and understand the specific format of the webhooks request, then YES. But most probably you would not be able to create Notes in another system (website) when a Note is created in Pipedrive without any additional development on that website.
If I understood your question correctly then you should be able to accomplish that by using some 3rd party integration platform like Zapier.
Hope this helps