1. You will find out what spiritbond is when you do the Materia-related quest. But in short, when you wear any equipment and do some stuff, like, kill monster, gather items from DoL class, craft something on DoH class, the equipment will gain a tiny bit of Spiritbond with you. When the Spiritbond is full, it can be turned into a Materia.

2. Materia is a new kind of item which can have different stat bonus, and can be meld (put into a slot) on a piece of equipment. Dated item won't have an open slot for a Materia. Most of the new equipment will have a slot for Materia.

3. I can't answer the Grand Company question because I was already overranked when I started GC quests.