She loves her cousin and he has proposed to her but he does not pray apart from Jumu’ah (Friday prayer)

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Check below answers in case you are looking for other related questions:
Love which ends in marriage – is it haraam?
Can a Suitor Lie to the Non-Muslim Family of the Girl He Wants to Marry and Say He is Unmarried

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Related Answers:
If a woman is impressed with a man’s character and religious commitment, can she offer herself to him for marriage?
She has received a proposal from a young man who smokes – should she agree to marry him?
He kissed his fiancée and touched her; is she haraam for him?
Love which ends in marriage – is it haraam?
Can a Suitor Lie to the Non-Muslim Family of the Girl He Wants to Marry and Say He is Unmarried

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