>>23
The number sqrt(2) is computable, yet requires infinite memory and infinite time to compute for obvious reasons.
The program wouldn't halt, so no, the entire number is not computable in that sense. A computable number is understood to be one for which a program can produce any desired digit (and then halt), which is possible for sqrt(2). The result is finite use of memory and time.
The input and output both require only finite memory
Given a continuous range, there are infinitely many possibilities for the values. Logically, these cannot all be stored in some limited number of digits.
>>25
Then the model would only be an approximation of reality, and therefore it wouldn't say anything about the computability of reality.