Is it permissible to stand at the grave after burial to supplicate to Allah and seek His forgiveness for the dead person?
Yes, it is not only permissible but also Mustahab (desirable) to do so. It has been reported by (Part No. 9; Page No. 94)
Abu Dawud, and
Al-Hakim who authenticated it on the authority of
`Uthman (may Allah be pleased with him):
Whenever the Messenger of Allah (peace be upon him) finished burying the dead, he used to stay at his grave and say: 'Seek forgiveness for your brother and beg steadfastness for him, for he will be questioned now.'