For point 2: I always got the impression that they did blip out when summoned. There's hundreds of them out there, but they've had thousands of years. And while we view it as imprisoned, they say they're keeping them safe (and from hurting themselves possibly I think, but I may be misremembering that bit). So they're stopping them from wandering around by keeping them locked up, but it's not trying to keep them all there forever. They just feel honor bound to take care of them. That's their ultimate goal, not to round them up.
On top of that, I'm not sure, like Syl when she's just being her little blue self hanging out with Kaladin is also in Shadesmar at the same time. I don't think it's like with lower spren where we're getting a peek at them on the other side. I think they're all the way over. Otherwise, in Oathbringer we probably would have seen Timbre, Ivory, and maybe Wyndle and Glys just hanging out on the cognitive side around Theylan City when Kaladin and the gang showed up. But it hasn't been verified, so who knows? Sanderson is pretty good at coming up with good reasons for stuff in retrospect.
It's also possible that their functionality requires them existing with a foot in both worlds, so to speak. They're not dead spren nor typical living spren. They're willfully imprisoned in some special way. Like, the Oathgate spren are the Oathgates, and seem like they're more responsive, but we know it's the same process as the Soulcasters and they're basically inert. Sanderson has said they're something like Shardblades, but he doesn't say they're just like Shardblades. They do act differently and affect things differently. Presumably they just work differently.