Many believe that he passed away in a battle when trying to restore some peace between non-benders and benders.
Yes, this has come up every now & again, but there's never been any actual evidence for it.
There have been many [...] hints that Sokka and Suki broke up on bad terms.
Doesn't list any.
The theory is: Suki become an equalist developing into more extreme measures and mentality
Before the Equalists even existed? Whose theory? Sounds like a "careful not to cut yourself on all that edge" moment, really.
I don't think she's ever disliked bending but has been through discrimination because she's not a bender.
When?
I feel like if they were together when Sokka passed away, she would've been shown or at least mentioned by Katara or someone close.
But she is mentioned by outside sources. Mike & Bryan describe them as "moving to the suburbs," & she comes up in the Legacy book, which is written from an in-universe perspective.