The imaginary unit [tex]i[/tex] belongs to the set of complex numbers, denoted by [tex]\mathbb C[/tex]. These numbers take the form [tex]a+bi[/tex], where [tex]a,b[/tex] are any real numbers.
The set of real numbers, [tex]\mathbb R[/tex], is a subset of [tex]\mathbb C[/tex], where each number in [tex]\mathbb R[/tex] can be obtained by taking [tex]b=0[/tex] and letting [tex]a[/tex] be any real number.
But any number in [tex]\mathbb C[/tex] with non-zero imaginary part is not a real number. This includes [tex]i[/tex].
I'm not sure what you mean by this part of your question. It is possible to represent any real number as a complex number, but not a purely imaginary one. All real numbers are complex, but not all complex numbers are real. For example, 2 is real and complex because [tex]2=2+0i[/tex].
There are some operations that you can carry out on purely imaginary numbers to get a purely real number. A famous example is raising [tex]i[/tex] to the [tex]i[/tex]-th power. Since [tex]i=e^{i\pi/2}[/tex], we have
[tex]i^i=\left(e^{i\pi/2}\right)^i=e^{i^2\pi/2}=e^{-\pi/2}\approx0.2079[/tex]
