What language do Muslims in non-Arab countries use for prayers? I know the Qur'an is not translated to, say, Farsi, but do Farsi people pray in Arabic or in Farsi?
Prayers could either refer to the ritual five daily Salat(s) (a concept similar to the Canonical hours in Christianity), which are prayed exclusively in Arabic. Though historically there might have been short-lived dissenting opinion and practice but the grand consensus has stuck with Arabic - the language of the Quran whose recitation is an obligatory part of the Salat.
However, the non-ritual prayers (talking to your Lord and seeking help) can be in any language or even no language at all.