I’m pretty the curvature of the universe has actually been measured to be very close to 0, within margin of error, which would suggest an infinite universe. (It doesn’t prove it by any means, though. The curvature could just too small to measure.)
However, the observable universe is indeed finite, due to the speed of light being finite.
Do they? There’s broad consensus on the size of the observable part, but what’s beyond that is surely more speculation than science.
Based on observations it seems that the universe curves in on itself. And is thus finite.
I’m pretty the curvature of the universe has actually been measured to be very close to 0, within margin of error, which would suggest an infinite universe. (It doesn’t prove it by any means, though. The curvature could just too small to measure.)
However, the observable universe is indeed finite, due to the speed of light being finite.