1. Maybe, but they’re normal steel swords with lots of Investiture, not godmetals.

I don’t have good answers, so I’ll speculate with a bit of possibly relevant information. I hope someone asks Brandon about these, as it’s really interesting.

1. I’m not sure, but considering that Shardblades are made of godmetal and cannot go to the Cognitive, other godmetals may be the same. Some speculation here suggests that Honorblades could travel normally to Shadesmar, which would be more applicable.
2. Again for Shardblades, the deadeyes disappears when the Blade is summoned, so I think the spren would not have any visible Cognitive presence. That might only apply when they become a Shardblade, though. On the other hand, other fabrials, such as Soulcasters, the Sibling, and Oathgates, are still visible in Shadesmar despite having a Physical presence, so that could be wrong.
3. I’m guessing you can kill spren with it, but I could be wrong. You could definitely kill humans, but that’s just because it’s a knife, not because of the anti-Investiture.