Can network attacks manipulate Bitcoin mining difficulty?

Is it even possible to attack nodes to mess with Bitcoin's difficulty adjustment by sending wrong timestamps? Like, can we really screw with the system that way?

Nah, that's not how it works. Difficulty is set every 2016 blocks, which is about 14 days. If you somehow get all nodes to lag a week behind, difficulty goes up to keep that 10-minute average. Trying to make it seem like 28 days passed? That's just gonna make difficulty drop, but honest nodes will reject your blocks. You'd be wasting your hash power on a useless fork.

Check out this related thread. Can average block time calculated every 2016 blocks be manipulated? But honestly, I doubt Bitcoin Core would accept a timestamp from another node if it's way off.

I get what you're saying, but if you had enough control over nodes to make the median timestamp look different from the actual time, could that work? Maybe?

Short answer: No. Longer answer: Difficulty is based on the last 2016 blocks. If your timestamps are way off, other nodes won't even look at your blocks. Current difficulty is what matters. If you somehow pull off some crazy stuff and make it work, you'd just have a fork coin that nobody cares about.