A creature “fights” when an effect instructs it to fight. Dealing combat damage isn’t fighting.

You draw just one card as Neyith’s first ability resolves, no matter how many creatures you control fought or became blocked.

While resolving Neyith’s last ability, you can’t pay multiple times to double a creature’s power more than once or to double more than one creature’s power.

If an effect instructs you to “double” a creature’s power, that creature gets +X/+0, where X is its power as that effect begins to apply. If its power is negative, instead it gets -X/-0 where X is how far below 0 its power is. The value of X won’t change if another effect alters the creature’s power later in the turn.

Only one creature is required to block the target creature. Other creatures may also block it and are free to block other creatures or not block at all.

If the target creature has menace, two creatures must block it if able.

The defending player, not you, chooses which creature blocks the target creature.

If each creature the defending player controls can’t block for any reason (such as being tapped), then the target creature isn’t blocked. If there’s a cost associated with blocking the target creature, the defending player isn’t forced to pay that cost, so it doesn’t have to be blocked in that case either.