Faustina

It's hard to be certain since there is no legend showing on the reverse. If you can make out any letters, it might be useful. In the meantime, I think your coin may be:

Faustina I AE Sestertius. DIVA FAVSTINA, draped bust right / AVGVSTA S-C, Ceres standing left with short torch and corn ears. RIC 1118, Cohen 88. Take a look at this image and see if you think it looks like your coin: http://wildwinds.com/coins/ric/faus...RIC_1118.jpg

There is no reason to believe your coin is not genuine. The condition is poor so the value will be low. Perhaps$5-$10 I should think. Sestertii are desirable coins because of the size and weight. They are also the more common coins used by the common man, and thus, they are generally more worn than their silver and gold counterparts. Most collectors, however, want coins that are attributable, and even with my attribution, it's questionable. I hope this answers some of your questions.

I agree that the edge looks suspect, other than that it looks fine to me.

I wonder if it has been set into jewelry at some point and that that was what caused the 'odd' edge. Perhaps some kind of escutcheon or mount surrounded the coin in the past when it was worn as a necklace

Looking at the top section on the reverse there appears to be some type of pattern, possibably form another coin. I wondering if this coin was struck over another one?