Firstly (this is a general discussion; theories and the math behind them takes up to much time and space {no pun}), your initial statement about the size of the Universe implies there is a "size". The fact is that the age and therefore the size of the Universe is dependant on a number of factors, but one of the most significant is the Hubble Constatnt about which there is a lot of disagreement as to it's value. By disagreement I mean the difference between 50 kms/Mpc and 100 kms/Mpc, or 100% of it's estimated value. This means that it's possible, depending on the actual value of H0, that we can never see the original light emitted at the creation event since the universe is expanding faster than the ability of light , at its speed (C) to to reach us.
So, therefore, my answer to your first poser would be... unknown... and unlikely to accomplish your proposition. Secondly... how big? My response would be "When?" We don't know now and can't know when there's no non-speculative way to measure it.
The Universe is not infinite, by any definition that includes a beginning as a component, which the commonly accepted definition of "Big Bang" does.
Lastly, you seem to imply that if the structure of the Universe is one way or the other that somehow inflation would not be part and parcel of whatever the morphology actually is. Big Bang inflation at around 10^-32 to 10^36 seconds is pretty well established mathmatically and the geometry of the universe follows on that event and the true value of Hubble.... A lot of discussion about the geometry, but most likely it's flat in my largely uninformed opinion...



