Yes, because it has a finite number of digits and can therefore be written as a ratio of integers. If you meant to put a "..." at the end, it would still be rational.
Let x = .232323...
100x = 23.232323...
100x - x = 23.232323... - x
99x = 23.232323... -.232323...
99x = 23
x = 23/99
.232323... = 23/99
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It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Yes. Any rational number divided by another rational number is also rational.