If we know the universe is expanding in whatever direction we look, can't we reasonably estimate where the 'center' of the Universe is?
Is the rate of expansions in all directions the same?
The speed that a galaxy moves away from you is larger the further away the galaxy already is. This is most consistent with an expanding universe.
I find the following mental picture helpful: Imagine a balloon, with lots of little dots painted on it. If you inflate the balloon, then every point is moving away from every other point. Where would the "center" be? Pretty much everywhere.
Wikipedia kindly presents four models you can use to visualize the expansion of the universe. All of these are meant to explain why we think the universe is expanding, yet we think there is no center. Everything† moves away from everything else, with expanding velocity proportional to the distance.
† Bound objects—in particular galaxies—are held together by binding forces like gravitation and therefore do not expand internally.