Answer

In the Name of Allah, Most Gracious, Most Merciful. 

All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.

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In this fatwa:

1- Performing funeral prayer at graveyards, when there is a need for that, is permissible.

2- As for other prayers, graveyards are not meant for that, and this should be avoided, generally speaking.

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Answering your question, Sheikh Mustafa Umar, President of California Islamic University, states:

Performing funeral prayer at graveyard, when there is a need for that, is permissible. This would happen when the funeral prayer was not performed in a mosque or elsewhere and the body reached the burial site already.

As for praying other prayers at a graveyard, this generally should not be done since the Prophet said, “All the earth is a mosque apart from the graveyards and bathrooms.” (At-Tirmidhi and Ibn Majah)

Almighty Allah knows best.