Can you use Egyptian god cards in a duel?

Unfortunately, the Egyptian God Cards have never been allowed in Yu-Gi-Oh! tournaments. But, if you duel with your friends, you can use any cards you want, even the Egyptian God Cards, and completely ignore the Forbidden/Limited Card lists.

What Egyptian God Card does Yugi get?

This card is also shown when Kaiba formulates to himself his plan on defeating Yugi and Yami Marik, winning their respective Egyptian God Cards ("Slifer the Sky Dragon" and "The Winged Dragon of Ra"), and becoming the number one Duelist once again.

Can Egyptian god cards be destroyed by card effects?

The opponent cannot equip cards to the "God" Cards. They cannot be returned to their controller's hand. They cannot be destroyed by card effects of non-"God" Cards. However, it seems they can be removed from play (as Yugi removed from play "The Winged Dragon of Ra" with "Ragnarok").