I need help with a quest.. Plus many questions

[Niwashi]

there are a ton of confusing things that are never explained in the game and are very vague how to do them such as dying gear,

Dye system is unlocked by the level 15 sidequest "Color Your World" in the Vesper Bay area of Western Thanalan.

how to start converting gear into materia and putting it into gear.

Converting old gear into materia is unlocked by the sidequest "Forging the Spirit". It requires level 19, but doesn't matter on which class.
Melding materia onto new gear to use its properties is unlocked by the sidequest "Waking the Spirit". It requires you to be level 19 or above on a crafting class that can make gear (i.e. any of the crafting classes other than Culinarian).
Over-melding (i.e. melding more materia onto an item than it has slots for) is unlocked by the sidequest "Melding Materia Muchly". It requires you to be level 25 or above on a crafting class that can make gear.

All three of these quests are at the Bonfire area of Central Thanalan.

I don't understand the the whole field gear thing vs battle gear.

It's just a way of categorizing gear according to whether its stats are designed to aid combat classes (battle gear) or crafting/gathering classes (field gear).