Dear Akinbo,
Shannon was a mathematician and it is logical to follow his context ( not Wheeler brave speculations ) to understand bit.
In arithmetic we start from the positive integers ( 1,2,3,4,5,6,...) and from the ideas of addition, multiplication,substraction and division. It is easy to test that these operations are not always possible ( 4 - 29, 5 - 7, 2 - 8, 4/29,5/7,... etc )unless we admot new kind of integers ( negative numbers, or more generally, rational numbers )If we include root extraction and the solution of equations, we can find some operations are not possible also unless we admit a new kind of numbers. Mathematicians had found that the extraction of the square root - 1 is not possible unless we go further and admit the complex numbers ( as is known, following mathematicians Einstein, Heisenberg and Schrodinger introduced the square root of - 1 in physics ).Thus,it is practical and productive everywhere ( even philosopher Immanuel Kant made an attempt to introduce negative numbers in philosophy ...)
Complex numbers are sometimes called imaginary.Complex number is not number in the same sense as a rational number ( used by Shannon for bits )It is a pair of numbers (x,y), united symbolically in the form z = x + yi . Hence, it is easy to see, that when y = 0 we say that z is real ( special term for 'post-rational numbers' ), correspondingly, when x = 0 then z is pure imaginary.
Next step.
let ax + by +c = 0 be an equation with complex numbers ( coefficients ). If we give x any concrete complex value , we can find the value of y. Set of pairs of real and complex values of x and y which satisfy the equation is called imaginary straight line, the pairs of them usually are called imaginary points and are said to lie on the line. When x and y are real, the point is called a real point; correspondingly, when a, b, c are all real, the line is defined as real line.etc Hence, we can easy deduce answers for questions 2 and 3.