No because that would be your cousin
Your sixth cousin is definitely a relative, but a distant relative. There are many relatives with whom you have no relationship, and many people who are note related to you with whom you have relationships. If by 'count' you mean does it make having an intimate relationship illegal or immoral, no.
Yes it is, provided that you and they are 16 years old or older, or over 17 for male homosexual relationships in Northern Ireland.
intimate register
The two were intimate friends, and they went out together every weekend.
informal
Intimate Strangers was created in 2004.
The Intimate Stranger was created in 1956.
The Intimate Sessions was created in 2006.
Intimate Theatre was created in 1931.
Intimate Connection was created in 1984.
Intimate Reflections was created in 1975.