What connects all the following:

1. One of the elements deciding hereditary
2. Hypothetical character for assuming and proceed in problem solving
3. One of the type of invisible means in medical diagnostics
4. Connected with Jesus Christ's birth, well, in a way
5. A well known type of factor / part of title of a famous television series

?

It appears to be:

the letter X

One of the elements deciding hereditary

Chromosomes are X and Y

Hypothetical character for assuming and proceed in problem solving

$x$ is a common variable name in algebra

One of the type of invisible means in medical diagnostic

An X-ray is used to diagnose internal medical problems and is not in the visible light spectrum

Connected with Jesus Christ's birth, well, in a way

Christmas is often abbreviated as Xmas

A well known type of factor / part of title of a famous television series

The X factor is a famous television show which finds people with its namesake

• Good Apep, quick too ! The last one has two items, one is X factor and the other is X Files (a famous television series of the past !) – Mea Culpa Nay Aug 27 '17 at 16:38