Does having sexual intercourse with a paternal cousin from behind, 10 years ago (when the questioner was 18 years old), count aszina, and what are the consequences?

What you have done is considered zina (fornication/adultery), as it is enjoyment of an unlawful vagina. You must repent, seek forgiveness, and conceal yourself, for the Prophet, peace and blessings be upon him, said: "O people, it is time for you to desist from transgressing the limits of Allah. Whoever commits any of these abominations should conceal himself with Allah's concealment, for whoever exposes his deed to us, we will apply Allah's كتاب (law) upon him." You are not obligated to do anything further if the woman was compliant with you.