Terumah Tidbits from the Rambam

1) "Because of my grandson the kohen gadol, I can't eat terumah. Who am I?"

A kohenes is allowed to eat terumah. If she marries a yisroel, she is no longer allowed to eat terumah. If her husband dies, she is again allowed to eat terumah, unless she bore a child to her yisraeli husband. If the child dies, also, she is again allowed to eat terumah, unless the child already produced a child of its own.

Hence, a kohenes marries a yisrael and bears him a daughter. The daughter marries a kohen and bears him a son, who is chosen to be kohen gadol. Even if the original kohenes loses her husband and daughter, and even though her only living descendant is a kohen, she is still prohibited from eating terumah, because her living descendant causes her to maintain a connection to her deceased yisraeli husband (unless she gets remarried to a kohen).

Interestingly, if the daughter were still alive but lost her husband, the existence of her son the kohen gadol would be the sole reason that she would still be allowed to eat terumah. See Rambam Hil. Terumos 6:11.

2) "I can eat terumah nowadays. No, really. Who am I?"

Although terumah min ha-torah is only in Eretz Yisroel, the nevi'im decreed that it also be observed in Bavel, because it is close to Eretz Yisroel and has frequent travelers to and fro, and the chachamim ha-rishonim decreed that it also be kept in Egypt, Amon, and Moav, which surround Eretz Yisrael. (Rambam 1:1)

Since this terumah is entirely rooted in a gezeirah d'rabbanan (as opposed to, I suppose, terumah in Suria or terumah bizman ha-zeh in Eretz Yisroel, which are perhaps gezeiros d'rabbanan that have a stronger connection to the din d'oraisa), the prohibition for a kohen who's tamei to eat terumah only applies to one who's intrinsically tamei - ba'al keri, zav, zavah, nidah, yoledes, or metzora - and not to one who extrinsically tamei - i.e., through maga, masa, or ohel. Hence, if a kohen (or kohenes) were to acquire terumah that grew in certain sections of Jordan, Egypt, or Iraq, he would be allowed to eat it once he was tovel to remove any intrinsic tum'ah that he might have. The Ra'avad, though (and the Rambam could perhaps also be read this way), states that this heter only works for a katan or a ketana who has a chazakah of tahara from tum'os keri and nida, because of a gezeirah on gedolim metuharim because of gedolim who are intrinsically tamei (Rambam 6:8-9).