tl;dr It's a loop because we can't make a magnifying glass big enough to see a single point.
1) He gave himself the coordinates to Nasa when he realized he could not change the past using the tessarect. He was simply put there to find a point in time to tell Murphy the data. He wanted himself to stay behind with Murph, but he could not change the past, and instead settled on ensuring the future WILL happen.
2) He found Nasa using the coordinates he sent himself from outside time. He gave himself the coordinates to NASA to make sure he would eventually repeat the same process. It's a loop so dont think too much of it.
3) There isn't an easy way to explain this part, so I'll explain the best I can. We are three dimensional beings, right? We can move in an XYZ plain (Forward, sideways, up/down,). However, we can only perceive in two dimensions. we only see a flat image (Take a ball. You can't see every point on the sphere in true depth. You only see one side of it, which makes it a circle, a 2 dimensional object).
To see in three dimensions, you would have to be a fourth dimensional being. However, you still can't see time as it is at this level. You would only be able to move forward and backward in time, never being able to change the outcome of a situation. So let's go up to five dimentions.
Being a fifth dimensional being gives you the ability to move parallel to time and observe multiple outcomes.
Now as a three dimentional being, you can create three dimentional objects and give properties to them. Slap a few peices of wood together and you got yourself a chair, right?
Well, when humanity eventually evolves into these 5th dimentional beings, they needed to ensure their evolution was set in stone.
Jumping back to the three dimentions, remember what I said about you only seeing in two dimentions? Well another thing to add is you can't see infinity below you either. You can only see down a single dimention. So you can't see a one dimentional object; a line. You can't also see a point in that line (a 0 dimentional space).
Well, as a fifth dimentional being, you can't see a 3 dimenational point in a fourth dimentional line. That's why they chose cooper, a 3d human, to find a point in a 4th dimensional line.
The tessarect itself is just a 4th dimentional line folded in multiple directions.