No, Satan does NOT... believe on Jesus Christ as His Saviour. It's stupid to even insinuate such an idea as that.
Just as Satan tries to claim what doesn't belong to him, so likewise the false Jews like to claim to belong to Israel when they weren't born of the seed of Israel to begin with, but crept in among Judah as Canaanites and foreigners of the nations, and now pass themselves off as Jews.
This is why YHVH made His Salvation through His Son Jesus Christ's Blood shed on the cross only, and none other way, not being born of a seed, not by one's own wishing, and definitely not by foreigner seed claiming to be of the seed of Israel when they are not.