(a) according your nice explaination (insight 46) about the way that the RAMBAN and the RAN explain the "partnership" i want to ask: in CHAGIGA the ramban should say - according his view - that half eved should be obligate in "rei'ya" because we can say in your words: "Each partner may choose any part of it and say that he is exercising his right that he bought (along with half of the value of the land) to use whatever part he wants". (and the ran should think the opposite)
(b) (and similarly: is their a way to say :din breirah in half eved??)
(a) Your question is according to the Mishnah Rishonah there, which says that a half-Eved is exempt from Re'iyah. The answer is that the Chiyuv of Re'iyah depends on actual ownership, and not just rights of usage. Even though half-ownership of an undividable property gives full rights of usage, nevertheless the ownership of the value of the item is still only partial. To be Chayav in Re'iyah, one must have full and total ownership of himself, with only Hash-m as his "Adon" and no other person as his Adon, as the Torah requires. Hence, both the Ran and the Ramban will agree that according to the Mishnah Acharonah, a half-Eved is exempt from Re'iyah. (This is clear from the Gemara in Gitin (42b) which discusses whether an Eved is considered the legal property of the master (and may eat Terumah if the master is a Kohen) or not, and it comes to no conclusive answer. That question applies only insofar as a Kinyan is concerned. The legal ownership of the half-slave does not affect the Halachah here, which depends on whether or not the person has any other master over him other than Hash-m.)
(b) According to the Ran, it would seem that an Eved owned by partners (or a half-Eved, owned partially by himself and partially by someone else) would be subject to Dinim of Bereirah. According to the Ran, when the Eved works for his master on one day and for himself the next day, that is a manifestation of the permissible type of Bereirah that the Ran discusses here. Of course, this, too, depends on the actual nature of ownership of an Eved as discussed in Gitin (42b).