Does this function use the same algorithm for sorting numbers array and strings array?
It might or it might not. That is not specified by the standard.
And if we use it to sort an array of strings which the total size of them is less than 100,000 characters, would it work in less than 1 second(in the worst case)?
It might or it might not. It depends on the machine you're running the program on. Even if it will work in less than 1 second in worst case on a particular machine, it would be difficult to prove. But you can get a decent estimation by measuring. A measurement only applies to the machine it was performed, of course.