A square number
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Only perfect squares can have an odd number of factors. The answer is 16. It has five factors: 1,2,4,8,16.
Yes. An even number is defined as being evenly divisible by 2 (no fractional answers, only integers). If an odd number has an even factor, then because of the above definition, this odd number must have a factor of 2. But you will be hard pressed to find an odd number that is a multiple of 2, because that is already the definition of an even number. So, odd numbers cannot have even factors and thus odd numbers always have odd factors.
No numbers in that range have an odd number of factors.
Only if an odd number of the factors are negative numbers.
Both odd and even numbers may have odd numbers as factors.