Is one allowed to eat food that was taken into the restroom (there is only a toilet – no shower nor bath)?
It is permitted to eat the food.
The Be’er Heitev (3:2) writes that one should not eat in a bathroom, implying that there is not problem in bringing food therein. This is explicitly ruled by the Salmas Chaim (3:9), though he writes that one should not bring food in lechatchilah.
This ruling (of not taking food into a toilet) is given by a number of authorities, because it is disrespectful for the food (see Tzitz Eliezer 14:2; Be’er Moshe 5:1; Har Tzvi 1:50; see, however, Magen Avraham 166:3, who implies that there is no problem of drinking in a merchatz).
The food, however, does not become prohibited for consumption.
In fact, even food that has been touched before netilas yadayim in the morning is permitted to eat according to many poskim (Mishnah Berurah, 4:14), though some are stringent (see Kaf Hachaim 4:20). This is all the more true concerning food taken into a bathroom, which does not have the same level of ruach ra’ah.
Moreover, although there might be room to equate a true beis hakisei of Chazal to the halachah of food touched before netilas yadayim, poskim debate whether our bathrooms are considered a beis hakisei or not, and this provides further room for leniency.
Moreover, in a bathroom that includes a sink as well as a toilet, and which is used for purposes other than excusing oneself, the issue of ruach ra’ah may not apply at all, and one can use the water from the sink even on a regular basis. A similar ruling is given by Teshuvos Vehanhagos 2:4.