Birkas hamozon minhogim (nusach, melody etc.)

According to the Rambam and the Sephardic Nusach it is said.
In Sidurei Ashkenaz this Posuk does not appear. In the Machzor Vitri the Posuk appears, but the Machzor Vitri is the French Nusach and not Nusach Ashkenaz, and, in addition, some times there was Sephardic influence which caused a change in the version of the Machzor Vitri, so we can not be sure that the Machzor Vitri himself recorded it as part of the Nusach.
R' Yaakov Chazzan of London (in Siddur Etz Chayim, which follows the French Nusach) writes "and one should not say Poseach Es Yodecho). This may mean that the French Nusach at one time was to say it (as seems from the Machzor Vitri), and he tried to change that, or that it was not the French Nusach ever, but some individuals tried to introduce it there, therefore he inserted a notice that one should not accept their change.

Michael FRBSH

The Nusach is Eliyoh Hanovi.
In the Rodelheim some words are different than the Nusach of the Rishonim (and in some other Siddurim of later prints the nusach is closer to the nusach of the Rishonim), and from Horachmon and on there are many changes.

Michael FRBSH

Until 300 years ago, Birkas Hamozon was said by one and he was Motzi everyone. Later on, when bentchers became more handy everyone started Bentching on his own, and two different Minhogim evolved - one was that everyone said (sang) together the Bentching, and the other was that one Bentches out loud and everyone Bentches silently.
According to the first Minhag there is no place for answering Omen (since everyone is saying everything together). According to the second Minhag, although by the Brochos people were Makpid to finish there Brocho before the leader, to answer Omen on his Brocho, no such Kpeida was for the Horachamon.

Michael FRBSH

I asked Rav Hamburger and he said he didn't do enough research on this topic yet. He didn't know of any other melody for Birkas Hamozon, except for several different variations here and there. (As far as the dating - it definitely isn't more than 300 years old, but it may be more recent).

Michael

Minhag Ashkenaz is to say shir Hamaalos and conclude with Tehilas Hashem. This is because there are two shitos with regard to what is the Limud Torah that one should include in his meal. According to Seder Hayom it is Shir Hamaalos and according to the Ar'i Z'l it is Tehillas Hashem.

The known and common Minhag Ashkenaz is to always say all of Birkas Hamazon (including Horachamons), both on Shabbos and week days.

Michael FRBSH

The Rosh was way before the time Bentchers became handy.
The Rosh lived about 700 years ago.

Michael