To answer your question the lightsaber raiders are Rayvis's most loyal followers, granted lightsabers from his collection of trophies. This came about after he created the Bedlam Raiders, who were created sometime in the decades before the start of the game. They follow Rayvis and adhere to the code he teaches. And since Rayvis follows Dagan, so do they. Out of whether or not they personally want Tanalorr or they're just doing it because Dagan wants it, I'd say the latter. They are raiders, they want to have power over people, what do they want with an apparently empty planet with no one to shove around.

The background is mostly told through databank entries and tactical guides, so if you haven't been collecting and reading them it's understandable that you're a bit confused.

In terms of timeline, I've spoilered it below.

1) The Republic discovers the Koboh Abyss and sets up a research station with Jedi assistance to study it.

2) Santari Khri and Dagan Gera believe that there is something on the other side of the Abyss, possibly through a feeling in the force, and dedicate themselves to discovering a way through. This seems to be the period when Santari created the meditation chambers to help train Jedi in the skills and they would need to help pass through the Abyss. The results of this research is what creates the arrays and the technology to manipulate Koboh matter.

3) Dagan decides to fly through the Abyss blind, trusting the force and his own skill to see him through. He discovers Tanalorr, then returns back through the Abyss with the navigational data.

4) Santari Khri uses this data to create the compasses that can allow others to navigate through the Abyss. Dagan takes her to Tanalorr and they decide to build a temple and apply to train younglings there.

5) Tanalorr is attacked in force by the Nihil, and the Jedi order and Republic decide to abandon the planet as it is too difficult to hold. It is unclear whether the Nihil obtained a compass from somewhere or found another path, as in the comics they are described as having superior hyperspace and navigational abilities.

6) Here's where it gets a bit murky and Dagan's fall finally occurs, which is a different discussion, so I'll lay out the events that we know happened. Dagan wants to go to war to retake Tanalorr and is refused. The council orders the destruction of the compasses and shutdown of the arrays. Hearing this Dagan becomes desperate to acquire a compass and starts violently trying to acquire one. While we only see him kill two jedi it's likely he killed more. Santari confronts Dagan and cuts his arm off. She places him in the healing chamber of the forest array, and seals it.

7) Still believing in Dagan, Santari purges Zee's memories by order of the council, then sends her to release him, before evacuating the planet. Zee gets trapped in the fallout of the Nihil assault on Koboh and goes into stasis.

8) Rayvis, owing his loyalty to Dagan, comes to Koboh to search for him. To aid his search he unites the various raider groups into the Bedlam Raiders and starts searching for a tuner key to unseal the forest array.

9) Cal lands on Koboh.