IIRC we haven't, but we did see Nalan use a regrowth fabrial on Szeth.
Besides, we know that Kaladin can use stormlight to heal from shardblade wounds, it wouldn't make sense if the more powerful version of such couldn't.
And the lightweaving hung around constantly for years making shady deals, beating up maids and ultimately killing Shallan's stepmom all on it's lonesome? Unlikely.
When you immediately recognize that the guy sitting next to you in class is wearing a SA shirt, and start a conversation with him about the cosmere.
Edit:
That depends. How much of a sanderfan are you?
Except in order for something to be investiture like how it was as part of Adonlasium, it would have to contain intent from all of the shards. The energy analogy fails because it doesn't have any consideration for intent.
Also, this WoB seems to imply that the surges themselves are part of Roshar magic in general. If this is the case, then surgebinding Dalinar did wouldn't drive out Cultivation's influence.
(Source)
Surgebinding seems to be a very 'mixed' system. I don't think it's correct to think of Honor's surgebinding in opposition to Cultivation's surgebinding. It's a cooperative system not a competitive one.