So how do the Knanaya view, say, the Armenians? Do they consider them fellow Christians?
These comments are essentially limited to the faithful of the Catholic and Orthodox Churches; there is not a lot of material available on the small Knanaite bodies within the Protestant Churches that have a presence in Kerala. The Knanaites' views of those who are members of any of the Apostolic Churches are not really any different than those of their co-religionists (whether those be Orthodox or Catholic). As a whole, they are as accepting of other Oriental Orthodox and Oriental Catholics as would be the case if they were not Knanaites. They just simply don't intermarry with them, not if they wish to retain their standing in their ethno-ecclesial community, and they typically would be unlikely to worship with them. As I'll explain, absent a parish of their own particular form, they would worship with other Indians of the Church in which they are a distinct etho-cultural subgroup.
In both the Orthodox and Catholic instances (Syrian Orthodox Jacobite Indian Church and the Syro-Malabarese Catholic Church), they have their own parishes, canonical jurisdiction, and hierarch. Separate parishes essentially date from time immemorial. The distinct eparchy and hierarch in each Church date from around 1910-1911, when both Churches made those provisions. In those few instances where Knanaites are geographically separated from their parishes, they'll worship with others of their own Church - but that is pretty much limited to the diaspora and even there, they tend to gravitate to areas where others of their ethnicity/culture have already settled, as did most of our ancestors when coming from the 'Old Countries' (in the neighborhoods dubbed 'Little Araby', 'Little Russia', etc).
In the US, neither the Orthodox (unless things changed recently) nor the Catholic Knanaites have their own bishop. However, each has a Knanaite vicar within the eparchy of their respective Churches who has superintendency of their parishes. (Last I checked, there were 10 parishes in the Vicariate for the Knanaite Catholic Community in North America, a suffragn jurisdiction of the Eparchy of St Thomas the Apostle in Chicago of the Syro-Malabars.)
The smaller groups within the Syro-Malankara Catholic and Orthodox Churches do not have eparchies or hierarchs, but do have parishes. I'm not sure how the Syro-Malankara Orthodox handle that arrangement (other than that they do accomodate the Knanaite praxis) but the Catholic approach to it affords a curious situation.
The Syro-Malabarese Catholics (who serve according to the Assyro-Chaldean Rite) maintain parishes in 2 of their eparchies for Syro-Malankara Knanaites, in which the liturgical forms employed are those of the Malankarese Knanaites' ancestral (Antiochene) Rite, as modified to include the particular Knanaite usages. Fifteen of these parishes are subject to the autonomous Metropolitan Arch-Eparchy of Kottayam of the Knanaites; they are clustered in an Episcopal Vicariate for Malankara Knanaites, headed by a Syro-Malankara Knanaite prelate. As memory serves, there are an additional two such parishes situated in a non-Knanaite Syro-Malabarese eparchy.