Do I lose materia and equipment when I lose a character

That is the White Materia, used for Holy, the most powerful White magic in the game.

It plays an important role in the plot so the plot summary is in the spoiler below. If you want more spoilers, the plot related to it can be hound here on the FF wiki

The White Materia is used to summon Holy. This is the only power capable of stopping Meteor, which was summoned by Sephiroth using the Black Materia. Aerith goes to the Forgotten Capital to pray to Holy, but is killed by Sephiroth. It turns out that she did successfully summon Holy, but Sephiroth is preventing it taking effect. You kill Sephiroth, Holy emerges, but Meteor is too close to be stopped by Holy alone. The Lifestream is used to push Meteor back, allowing Holy to destroy it.

For the best way to get AP for materia, go to the northern crater. Once you get there, go to the bottom (the room just before you fight jenova), but instead of going further down, go to the left and enter. There should be an enemy called "Magic Pot". To beat them, you have to throw them an elixir and then on the next turn hit them. You will receive 1000AP per magic pot you kill.

Every maxed-out materia will get multiplied (even summon materia), with the exception of MASTER materia.