One time I was driving on a dark, lonely stretch of rural highway in Kansas. Middle of the night. I suddenly realize that there is this big, pulsing "thing" floating right above the tree line over a field next to the road. Looked like something strobing multicolored light from inside a cloud or something. No downdraft, so I knew it wasn't a helicopter. It wasn't moving, so it couldn't be a plane.
In that instant, I had to admit that now, here was some evidence for a phenomenon I had previously rejected. I almost stopped to take pictures, but I didn't. And that is when I crested a small hill that I didn't even realize was there. And on the other side, blocked from view, was a cop with his lights on behind the car he just pulled over.
Now, it was clear that the thing was just a low fog bank reflecting the cruiser lights that were blocked from my view. One additional piece of information recast the entire scene. I believe that most, if not all, weird occurrences like this ultimately stem from a simple lack of information. The rest I chalk up to the simple ability of the human mind to fool itself, especially in unfamiliar or stressful situations, and I am always wary of the way memories change over time.
Some reading on that last bit that I found especially fascinating: https://www.amazon.com/Invisible-Gorilla-How-Intuitions-Deceive/dp/0307459667/ref=sr_1_1

Not an insurmountable issue in the least, especially if you are willing to spend human lives to achieve your goals. You can get a lot done if you are willing to sacrifice tens of thousands of subjects in grueling slave labor.

Yes. None of that requires superhuman technology or intelligence. It just takes a bit of skill, planning, patience and lots of people to provide muscle.

Of course we could. And a lot better than the original designers. We aren't building pyramids because there is no point or profit to it, not because it is technologically insoluble.