No, satan is not a fallen angel. God tells us in the Bible that angels do not sin, so they cannot “fall”: angels only do what God wants them to do:
Bless the Lord, O you his angels, you mighty ones who do his word, obeying the voice of his word!
Angles obey what God says.
Likewise, Heb. 1:14 says that all angels are ‘ministering spirits sent out to serve for the sake of those who are to inherit salvation’. Angels are God’s workers and they only do what God asks them to do.
This goes against the idea that satan was once an angel who sinned against God.