Some of this could be explained via Kaladin's potential Resonance, part of Syl not knowing things is also probably from the fact that while this is her second bond, she lost most of herself in between.
As to #4, that's because the spren was almost entirely in the Physical Realm, allowing the Sylknife to interact with it like it would anything else.
The "something" that Dalinar grabs is probably raw Investiture, which I think is a direct result of the whole "I am Unity" thing, just on a smaller scale.