Yes.
I would call an odd number factor a factor that is an odd number. I would call a number with an odd number of factors a perfect square.
A square number has an odd number of factors, but a number with an odd number of factor pairs is nothing special.
A perfect square has an odd number of factors.
Square numbers have an odd number of factors, but beyond that, any odd number can be a factor.
square numbers
Yes, because each factor must have another factor to go with it, but the square root of a number can have itself as a pair.
There are infinitely many of them. The square of every odd number will be an odd square number.
1, 25
1 and 25
1 and 25
All odd numbers have odd factors.