Light Screen specifically protects against offensive special attacks, like Fire Blast; it doesn't protect against moves like Hypnosis or Sing, so genjutsu would still pass through it.
I forgot what Safeguard was, though, and you're right on that point.
If he uses Skill Swap on Sasuke's eyes, though, he'd either gain one or the other. They're two seperate abilities. Still, I think Sasuke can simply dodge the effect via Amenotejikara.
Taunt doesn't last very long, though, and it's unlikely Deoxys will spam it every chance it gets.
Gaara was only able to grab Madara out of his Susano'o by exploiting the fact that in the form that Madara was using, it was open at ground level, and the Susano'o's creator can freely pass through its protection. Psychic attacks would have to get through Susano'o first, much in the same way that the move Psychic can't bypass Substitution.
Sasuke's chakra reserves are actually quite high. He's able to spam Rinnegan and Sharingan abilities easily when he fought Momoshiki with Naruto, using Amenotejikara multiple times over the course of the fight, including what were previously said to be massive chakra drains with Chibaku Tensei, Susano'o, Enton: Kagutsuchi. This being after he did something else that was supposedly a huge chakra drain, opening a portal to Kaguya's dimension, and holding it open long enough for more than just himself to pass through.
Pressure is a legitimate issue, but this Sasuke is far superior to his teenage self, who was able to use nine Chibaku Tensei at once, strong enough to hold all 9 tailed beasts after putting them under a Rinnegan Genjutsu, this after fighting a long, tiring battle with Madara and then Kaguya--and then right after that, with no rest, he fought a day-long deathmatch with Naruto where he spammed multiple Sharingan and Rinnegan abilities along with high-powered ninjutsu with zero issue whatsoever (only using chakra absorption when both were on their last leg).
The Chibaku Tensei feats are particularly impressive, because remember--in an attempt to capture the rampaging Kyuubi/Naruto, Nagato literally became a shrivelled, white-haired husk, shortening his lifespan drastically in an attempt to mold enough chakra to create a single Chibaku Tensei strong enough to hold the Nine Tails at full power, and failed miserably.
I think he can handle Pressure, tbh.