October 2018 - last edited November 2018
@JimWUK I've moved this discussion to a new thread since it's diverged from simple introductions now. I can see you've been hitting and overcoming some obstacles! If you come across anything that is preventing you from progressing your main class story or chapters, you can post in the Technical Issues forum or submit a ticket by emailing support@swtor.com
November 2018
For this bug, it happens if you complete the heroic mission that the NPC offers if you talk to them which is "Friends of Old". If you finish this mission before turning in the mission you have "Unauthorized Transmission, Part II" then you cannot complete that mission as it's part of a sequence.
You will need to wait for the heroic mission to reset on Tuesdays. When the mission resets, speak to the NPC directly, he will give you the heroic mission again for "Friends of Old". Once you have that mission, speak to him again which will allow you to turn in the mission "Unauthorized Transmission, Part II".
Any future bugs you encounter can be reported to support@swtor.com as well.
November 2018
The area that you have unexplored is not grathan's estate. There is an area in the middle which I've highlighted that you need to go into an explore. Once you have done that it will fully show that map as explored.
For future reference bits and pieces of the map are designed to not show unless you fully unlock all areas of the map. See my attachment for what you still need to explore.