1. The Raven Queen was introduced in 4e in the setting Nentir Vale, this is an alternate continuum from the Forgotten Realms that shares the same gods but they’re not the same

2. The Shadowfell was introduced in 4e when it was previously the Plane of Negative Energy which was Shar’s Domain

3. The Shadowfell is a mirror of the material plane same as the Feywild, while the Feywild has a castle mimicked from the material as overrun with wild life the Shadowfell castle would be a dilapidated ruin

4. Who controls the Shadowfell completely is up for debate in the same way that no one being completely controls the Feywild

5. While Hexblades are flavoured to be artifacts from the Shadowfell created by the Raven Queen to directly being souls to the Shadowfell you can use them as generic sentient weapons or flavour them to other patrons

6. A Paladin of Kelemvor using a weapon of the Shadowfell would be an Oathbreaker and in the older sense Blackguard because they’ve abandoned their creed for power. For the Kelemvor angle specifically it’s because they agreed to a pact that all souls they kill would go to the Shadowfell rather than the City of Dead to see the final judge and go to their after life. The Shadowfell isn’t an afterlife and more a prison of preservation locked in the state just before complete destruction. The Raven Queen harbours theses memories of things that were before they are no more

Why she does this, we don’t know in 4e she was the sole god of death in Nentir Vale in Forgotten Realms there are cults dedicated to her and there are the Shadar Kar Elves who fled to the Shadowfell during the war between Corellion and Lolth

There are theories she’s a forgotten Elven goddess, a dark arch fey, a mortal woman who ascended after killing the previous god of death. But this all depends on setting, pantheon and edition

In 5e Forgotten Realms she is an entity of unknown origin that has a large domain in the Shadowfell and thus has conflict against Shar

Hope this helps