Hi Odetonoise,
You could read documentation first to understand differences between segment and marketing list, which might be helpful to you to work with transition towards Dynamics Marketing faster:
https://docs.microsoft.com/en-us/dynamics365/marketing/segments-vs-lists
For what you have tried so far:
1. There is no relationship between Segment and Contact, members of segment are populated with a unique concept: Segment Query,
therefore, we couldn't extract members from segment via advanced find.
To manage members, we need to stop the live dynamic segment and change filters, or change field value of contacts, then contacts who are eligible/not eligible will be added to/removed from dynamic segment automatically.
2. As you said, D365 connector is being deprecated, but we can instead use Common Data Service connector to connect to Dynamics instance.
Are you trying to add contact to segment in Power Automate?
If yes, we can perform an unbound action :msdyncrm_SegmentMembersUpdate to do it.

Please refer to documentation for more details about the action:
https://docs.microsoft.com/en-us/dynamics365/marketing/developer/extend-segments#addremove-contacts-to-static-segments
Also, we should notice that only static segment is supported to add/remove members programmatically.
3. According to the comparison table at the beginning, we can know that only segment is supported to deliver marketing emails to contacts.
If you want to send email to members in marketing list, you could build a static segment and query members from a specific marketing list,
then add them to segment.

Regards,
Clofly