Is the universe truly infinite?

We can measure qualities of spacetime that might be useful in answering the question though.
>3-D torus
uhhh no.
>There is a finite amount of matter in the universe, correct?
If the Universe is infinite, homogeneous, and isotropic, then yes. Data suggests this is true, but only really gives a lower bound for how smooth the distribution of matter is.
>with the speed given to it by the big bang
Incorrect. The kinetic energy of celestial bodies came from the gravitational potential energy of the once mostly uniform early Universe. Slight variations in the density created regions for matter to fall towards.
>So we have celestial bodies quickly moving away from each other in all directions
Only on very large scales does the inflation of spacetime overpower gravitational attraction of nearby matter. Our galaxy will never be pulled apart by inflation.
>the rest of your post
Read an introductory cosmology book.

Right. The reality is known as "spacetime."

>Most theories predict
Most theories leave this particular question open and explain the dynamics in any case. For example, General Relativity.

Why is that? Spacetime doesn't have to fit into a box. Why should it need to be finite?

We have no way of telling if the universe is infinite, as we simply don't have the time to find out.