In Background to the Daf for 2a, you explained the difference between a neder and a shavua, which was a useful explanation for me.
However, on daf 4b, it uses the language of "haomer l'chaveiro mudar ani," in a way that sounds more like a shavua according to the definition you provided than a neder. You said that a neder has to apply to a thing that the person owns, yet here he seems to be prohibited from a person, not a thing, by means of a neder. Does the language "mudar" include shevuot?
The case you mention, "Mudar Ani Lach" of the Mishnah, is referring to where he also said "she'Ani Ochel Lach" -- he specifically prohibited on himself the possessions of his friend. Where, however, he did not specify what he was prohibiting, it is taken to mean that he wishes to prohibit with a Neder both his possessions on his friend and his friend's possessions on himself. However, the Ran in many places explains that if one makes a Neder but uses the language of a Shevu'ah or vice versa, it takes effect for it is a "Yad" and although he did not say it properly it still takes effect (see Insights to Nedarim 2b:3).
Dov Zupnik