Yes it is permissible as long as there is nothing haram such as nudity or music.

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Nothing is prescribed. The sunnah is to Pray salatul Janaza. Kindly refer to the following link(s): https://m.youtube.com/watch?feature=youtu.be&v=fHxz7-tYn6w

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The custody is with the mother as long as she does not remarry. Kindly refer to the following link(s): https://www.youtube.com/watch?v=U5GK8Wk9LFE&app=desktop

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