Are we allowed to recite "Faatiha" at a funeral or for a deceased person?

If by Faatiha, you mean du’aa and prayer for the deceased, then the Janaaza Salaat is exactly for that.

There are four Takbeers in Janaaza Salaat. After the first Takbeer, the Thanaa (Subhaanaka Allaahumma) is recited. After the second Takbeer, Salaat and Salaam is sent to Rasulullah [sallallaahu alayhi wasallam] and after the third Takbeer, a du’aa of forgiveness is made for the deceased. The salaam is made after the fourth Takbeer. This is the way of du’aa established by Shari’ah for a deceased. Rasulullah [sallallaahu alayhi wasallam] and the Sahaaba [radhiallaahu anhum] made du’aa for the deceased in this way. There is no other way that is more blessed and beneficial to the deceased than the Sunnah way of Rasulullah [sallallaahu alayhi wasallam].

If by Faatiha, you mean the customary practice of du’aa after the Janaaza Salaat, then that has no basis in Shari’ah. Such an act is bid’ah and should be shunned. The deceased do not benefit from acts of bid’ah.

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai