Your question is rather a deep philosophical set of questions.
Can we be accurate in our measurements? Well, if two apples are always two apples, two inches are never two inches. Two apples are two apples even if one is twice the size of the other. But when you try to read two inches closer and closer, you end up meeting the Quantum principle of uncertainty where the end of your measuring tape's last particle cannot be predicted in both space and time.
I think that our problem is that, evolution has given us an understanding of space and time in order to throw a stone at a prey and eat to survive. Understanding the universe is not needed for best survival.
Is anything constant? Well perhaps but then, only in the eye of the observer. That is the main idea of Relativity: two observers can observe differently in their own frame of reference and yet, both are correct. Perhaps what is a constant for me is not for you.
A similar thought is when people ask what is at the "edge" of the universe and beyond it. Well ... as we know, we can only observe the universe as if we were at its center. Pretty much like the fish swimming in the ocean of a planet without continent would always be in the "center" of the ocean.
I think that the two main questions to the mystery of the universe are:
Are space and time finite or infinite? For example, is there a smallest unit of space under which nothing can be divided? Actually, the ethymological definition of the "atom" (indivisible).
And, is tomorrow already written? Or, does any possible outcome of an event exist in ... say, a parallel universe?
At the age of 66, I will never live to know the answers but I bet you are much younger than me and, perhaps, you will. If you do, can you send me an email at : email@example.com? ;-)