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No, 117 = 3313 and 117 ** 0.5 is about 10, so if you break the while loop, you won't find 13! But if you want to find out is a number prime, that will help.
If you do p.append([m,1]) break the while loop when i ** 2 > m it will be faster.
No.
Elegant solution but it looks like it obtains all the divisors to n, rather than just prime divisors.
It's still likely to break things downstream because n/i will have a float type rather than int, doing annoying things like producing unwanted ".0" in printed output and str() conversions.
Note in Python 3 it should be n // i
The only reason this Python 2 code did not break is that it's only running while n % i == 0, so it happen to be only feeding numbers that divide into whole numbers anyway.
nice job!