Is it permissible to perform Fatihah or to give offerings at an unmarked grave when it is not known whether anyone is even buried there or if the grave is that of a Muslim or non-Muslim?
It is impermissible to perform Fatihah or to take offerings at such a grave whose state is unknown to such an extent that no one knows whether it is a grave of a Muslim or a non-Muslim. Visiting the graves of the Muslims is a sunnah and performing fatihah is mustahab. However, visiting the grave of a non-Muslim is haram and even intending to send reward to a kafir is kufr.
Thus, any action that is undefined as being classed as a sunnah or haram or mustahab or kufr is indeed haram and unlawful.
And Allah ﷻ knows the best
Imam Ahmad Rida Khan رحمة الله تعالى عليه
Translation by Dr Musharraf Hussain Al-Azhari Translator of Majestic Quran, www.majesticquran.co.uk