Not always, but most of the time.
No. If one of the numbers is 0 it is less; if one of the numbers is 1 it is the same as one of them; otherwise the product is greater than either
The product of two digit numbers is always greater than either.
No. Their product is always greater than 0.
Whenever you multiply two negative real numbers.
The assertion in the question is simply not true.
Yes, if both the numbers have the same sign. But not if only one of them is negative.
Yes, yes it is. Because a mixed number must have a whole number in it. Therefore, being multiplied only makes it bigger.