1) if a person buys an eved (ivri) for a prutah--what is the giro-on starting the second year? 2) if a woman claims that an item (shova kessef) which has a market value of less then a shova prutah is worth more than a shova prutah for her is she mekudeshes with it?
1) Gira'on needs a Perutah, see Tosfos on 4b, DH me'Ikara. The Sefer ha'Miknah and Minchas Chinuch both question if Gira'on from a Nochri needs a Perutah, since less than a Perutah is considered Mamon with regard to a Nochri.
2)The Ran on 8b questions if it helps to assess something which is less than a Perutah to make it into a Perutah. However, on 12a he writes that it only works if the article in question is worth a Perutah somewhere else.