Yes, of course. In fact the product of any two numbers is composite unless one of them is 1.
Composite
The product of two prime numbers will be composite.
composite
If the number is a product of two composite numbers, it must be 16, which is the product of 4 and 4. The prime factors of 16 are 2, 2, 2, and 2. The smallest composite number is 4, so the smallest possible product of two composite numbers is 4 x 4 = 16.
No not always because composite numbers can be the product of 2 or more prime factors
If you mean the product, that's by definition. A composite number has smaller factors. If you multiply two positive integers, none of which is 1, together, then it follows that the product has smaller factors - namely, the numbers you multiplied together.
Any product of two or more odd numbers that are larger than 1. For example, 33 = 3*11 is odd and composite.
When the numbers are relatively prime.
There are no two "last" composite numbers. Just as with prime numbers, and all numbers, they go on for ever and ever and ever and ever ... ... .
Prime numbers have only two factors: one and themselves. By definition, your product would have more than that: one, the product and at least the two numbers that created the product. It has to be composite.
Public key encryption is based on composite numbers. In fact it is based on composite numbers which are the product of two very large prime numbers.