Infinity is the never ending, but not the never changing. I would say infinity (as in the common infinity ℵ0) is one more than the last finite number (by definition) so if you take one from it it becomes finite. Therefore the number can become finite even if it's a finite number you could only count with an infinite number of time. About time being still in some places, there is one place where time is supposedly still, the inside of a black hole, and even though we don't know exactly what happens there is common acceptance that time just goes very slow as if time were really still time would get exponentially slower the closer you got to a black hole but the curve would never get to infinity as it would have to get through the last finite number, something imposible in a finite distance. Therefore actually there is no infinity in the proper universe (I'm not really going to get into the multiverse). I hope that cleared some or all of your doubts! Bye!