1) Why were they built? They aren't a house or office building. They are very large for what and for who?
The pyramids were built for many reasons. As tombs, symbols of power, sites of religious worship, and as cosmic engines (clocks). The only mystery here is how do you not know this? The answers to these questions can be found in a sixth grade history book.
2) The precision of the stone blocks is unfathomable at that age of our understanding of human development. World class construction companies have said they would not even attempt to create such a building today. Some sites with 1000 ton blocks. And for what/who? How did they achieve such precision with out our modern day machines???
This is not true at all. It's well understood how the stones were quarried and cut into the shapes and sizes they needed. We've even found the tools they used to do this. Here's a short video on some of the techniques they used:
https://www.youtube.com/watch?list=PLfBAovcuRFSI4WO_FkviKEEPShE9tOBCd&t=379&v=3zkzZM51LyE
Also, the idea that we couldn't build the great pyramids today is absurd. The Great Pyramid is about 3,000,000 cubic yards. By comparison, the Panama Canal was built in 1903 and they moved over a 1,000,000 cubic yards . . . per day! And the precision needed for the water locks they built is far - far greater than anything in the pyramids.
3) Why did cultures all over the world independently develop such similarities with now way to communication with each other at all? No, it was not a planet wide pyramid competitions - you'd think so, but no.
What similarities? The pyramid shape? Are you surprised that separate civilizations also discovered spheres and cubes independently too?
A pyramid is the easiest three dimensional shape you can build. And it was the only shape that they could build with the materials they had to those kinds of heights.