Welcome here, Paul!
Only Basic plans have a .discourse.group domain.
Custom domain (to be understood as: any domain you own) starts from the Standard ($100/month) plan. 
Can you clarify what would be the goal of your forum? Is it a support forum?
How do you define an “expert”? What are their purpose?
Discourse has a group feature: https://meta.discourse.org/g
You could have an Experts group and put your expert users in it. You could then choose whether the group can be mentioned by other users or not. Like @lawblogger, but with a group name instead.
We also have an official assignment plugin that allow assigning topics or posts to certain people or groups:
But it’s hard to recommend features if we don’t have a better picture of what you are trying to achieve.
The search has filters.
https://meta.discourse.org/search?q=group:team will return all posts from members of the “team” group.
In the same way, https://meta.discourse.org/search?q=@codinghorror will return every posts from the user “codinghorror”.
There’s an official plugin that could fit: Discourse Subscriptions
It allows users to pay to access a certain group.
Your forum could have most categories locked for users not belonging to this group, so subscribing would unlock most of your forum’s content.
Note that the use of plugins is restricted for certain plans. Details are here: Plugin directory | Discourse - Civilized Discussion.
The assign plugin is available starting with the Business plan (assign).