Will I lose my account plating protection if someone attack me and I shoot bullets in backfire?

No. As defender you don't lose account plating protection. Only attackers.

Does account plating makes my account stronger as attacker?

No. Account plating makes only defending accounts harder to kill. Attackers have no benefit of it.

How can I see another player's plating level?

If you open the player profile of other player it will say his plating level.

When first Godfather comes and I didn't shoot anyone, will I still be under account plating?

Once first Godfather/First Lady rank appears in the game, a plating level will be removed from all players every 48 hours until it is completely removed.

Will i lose plating if I shoot family in the same city?

If there are two (or more) families in the same city they have plating protection towards each other with the plating level Very Low. If you shoot someone, you will lose your plating protection towards families that come from the outside as well.