I suspect really thinking in higher dimensions might be beyond us. We grow up in a world where the natural expression of dimensionality is 3D space, we have some inkling of time, and have managed to figure out space-time, but I think truly thinking in the 11 dimensions that some physicists have posited is just too unnatural, our brains are not evolved to cope.

Yes I think there are limits to what the human mind can know and understand. And I think there will be limits to what AIs will be able to understand.
For instance, I personally can't see how time and space are merged in spacetime. I mean, I know that they are merged, mathematically, but I can't feel/see/intuit it. I wonder if that's the same for everyone.

I think overtime humans would eventually start modying DNA to be able to select for higher intelligence to process more complex information than we are able to at this current point in time or we could potentially integrate our conciousness with artificial intelligence to give us exponentially growth in our ability to percieve or process information....so I think we do potentially have an unlimited scope for growth.

To plumb the depths of nature's mysteries is bound to take longer than the time it takes to pluck a chicken. And it's gonna require some pretty sophisticated, precision equipment. The kind of stuff that only a highly technological society can produce. All that goes out the window if civilization collapses. Now let's see. What could possibly bring about the demise of this shining city on a hill? Greed? Corruption? Racism? Superstition? Atavistic tribalism? How about a mix of all those lovely ingredients together with some feedback loop spiking global temperatures, some crop failures, a squeeze of jihad and a dash of thermonuclear war. That'd do it. Tick tock.

it we be impossible to reach a point of knowing if something we can't observe exists, so I am not sure if that's what you mean, but if so, then yes, Science is limited to our ability to observe, and nothing we can't observe can ever be known to us. I call those things basically "meaningless" to our every day lives, since without being able to measure any effect, observe any reaction, we cannot know what any of it is or means.

if you mean "could we eventually observe everything", then yeah, sure, so long as everything is measurable. IF the world is purely quantum interaction, then we can eventually observe every effect and draw accurate conclusions from them. IF there are aspects of the world beyond those things, we can't, and we won't ever know if they exist or not.