Is saying to someone, "I bear witness before Allah, the One, the Subduer, that I will not speak or discuss a religious topic with him unless his primary reference is the Qur'an, his secondary is the Prophetic Sunnah, and his third is the scholarly ijtihad (independent reasoning)," considered a vow? If so, what type of vow is it, is it obligatory to fulfill it, and is the expiation for an oath (kaffarat al-yameen) performed once to allow for continued religious discussions with him without repeating the expiation, or is the expiation repeated every time a discussion takes place?

If by the phrase "I bear witness before Allah" you intended an oath, then you have broken it by speaking with the person if their reference (i.e., their religious authority or affiliation) was not as you stipulated. You are consequently liable for expiation, which is only obligatory if you are certain that the oath has been broken. The expiation is not repeated with the repetition of the breaking of the oath, unless the wording indicates repetition, or it was intended, or custom dictates it. For the expiation of an oath, fasting is not obligatory except when one is unable to feed ten needy persons, or clothe them, or free a slave. This phrase is considered an oath, not a vow.