Official Discourse hosting only allows custom plugins on the Enterprise plan, and we have to assess the plugin code and determine whether or not a maintenance fee is required. Plugins can edit backend code, so we have to err on the side of caution when running anything custom on shared infrastructure.
We have a list of official plugins that are included on our hosting here: Plugin directory | Discourse - Civilized Discussion
Discourse Connect is included in all versions of Discourse by default, and if Lexicon uses our API that’s fine on our hosting as long as it’s not causing you to go over pageview limits or running into any API rate limits.
Yes, it’s possible. We have lots of customers that pass data from an external account via SSO into a custom field in Discourse. There’s some more detail in that topic: