Is the universe expanding at a n even rate?

The universe isn't actually expanding at all. The idea that it does comes from the original misinterpretation of galactic redshifts as being a doppler effect when, in reality, they are a scattering effect. The galaxies are not generally receding from each other. Their light simply loses energy through it's interaction with the molecular hydrogen that fills intergalactic space (see source).

If space expanded, as well as stretching out the energy of light radially causing distant galaxies to appear redshifted, it would stretch it out transversely causing a reduction in their surface brightnesses. This is not what we observe:

http://www.sci-news.com/astronomy/science-universe...

Expanding space would also stretch out the light curves of quasars (their oscillation in luminosity). No sign of this either:

http://phys.org/news190027752.html

There never was a Big Bang. This documentary may enlighten you:

https://www.youtube.com/watch?v=IFFl9S39CTM

"Is the universe expanding at a n even rate?"

Evenly between today, and all points in a past epoch, but expansion is accelerating in forward time.

For example between 4 and 5 billion years ago, expansion was slow. Between today and 1 billion years ago, expansion is faster.

It appears to be expanding equally in all direction.

It is accelerating.