More questions from a newbie

[Cherryblossoms]

1 - Keep up with your story quest line, it will lead you through it at level 20.

2 - Some stages of the relic glows, others dont. There are non-relics that glow as well. You can try some on from the market board.

3 - Only disciples of the hand can affix materia but you can request they do it for you.

[Nerael]

1 - Keep up with your story quest line, it will lead you through it at level 20.

Just a quick addition. That's Story quest level 20. Not Character level 20. On first playthrough most people are around 23 when they get the Chocobo.
(You get the chocobo quest right after you join a Grand Company)