Do you get the free access spells from all the paths that you have invested Magic Level points up to the spells you know or you have to choose one of the paths you know and take as much free access spells as your level at that path allows?

For example, I have 30 Magic Level in Light and 20 in Earth.Do I know all the free access spells that are inside the first 15 of the Light path and all the free access spells that are within the first 10 of the earth path or only the Light ones or Earth ones?

You are able to choose spells from the free acces area for both paths that you have, though some free access spells are restricted from certian paths. Wether you actually know your complete lvl in spells is up to the GM.

And does the option of choosing specific spells freely by investing Magic Level points allow you to choose a spell that it is from a path you have not invested Magic Level points.

For example, I have 20 Level in Earth and 10 in Light and I want to learn Fireball from the Fire path is it possible?

Yes that is right, providing you are not implying that you want to obtain Fireball with a Free Access spell slot.

Ie. Yes you can purchase Fireball by investing the required Magic Levels to purchase that spell individually outside of its path.