Question

what are normalised and orthogonalised wave function

Answer 1

A normalized wave funtion means that the probability that the particle is found in the considered domain is equal to 1 and thus the integral of the square of the wave function in the domain is equal to 1 (remind that the wave function is a function of complex variable).

As for orthogonality it is just a sequence of spectral theorem for hermitian operators in finite dimensional space. Hermitian operators always have a complete set of orthogonal eigenfunctions (at least up to a unitary transformation). As a solution of stationary schrodinger equation is an eigenfunction of hermitian operator, it will be orthogonal to all the other solutions.