1) As far as I can see, Rav Hamnuna is not connected to Rebbi Yehudah. The reason I say this is that Rav Hamnuna said that the Mishnah refers to pieces of garments less than 3x3 Tefachim large. That means that they are not considered to be a Kli, because less than 3x3 is not a vessel. If so, this has no connection to Rebbi Yehudah, because the Din of Rebbi Yehudah is specifically about Kelim (or broken Kelim). This is why Rebbi Akiva said (end of 28b) that since the folding is effective, the garments are no longer considered as Kelim and, therefore, even according to Rebbi Yehudah one may light them up because one is not lighting a Kli but simply a piece of wood.

2)

(a) The first Ukimta in the Mishnah is that of Rebbi Elazar and Rav Ada bar Ahavah, who say that the Mishnah refers to garments of exaclty 3x3 and that everyone agrees with the Din of Rebbi Yehudah. Then, the Gemara asks a contradiction in the position of Rav Ada about whether or not he agrees with Rebbi Yehudah.

(b) Afterwards (beginning of 29a), the Gemara cites Rava who explains why Rebbi Eliezer maintains that one may not light with the garments of the Mishnah.

(c) Then, the Gemara leaves its discussion of the Mishnah for the time being and deals with the dispute between Rebbi Yehudah and Rebbi Shimon about lighting up broken vessels on Yom Tov, and related disputes between Rebbi Yehudah and Rebbi Shimon. This discussion about Rebbi Yehudah and Rebbi Shimon takes up most of 29a. Only when it finishes that discussion do we finally get back to explaining the Mishnah and citing Rav Hamnuna's explanation.

(d) This is not unusual, generally speaking, that the Gemara digresses from the original topic into a secondary issue, and takes a while before it returns to the original topic. I do not think that the fact that there is a gap between the original discussion of the Mishnah and Rav Hamnuna's Ukimta of the Mishnah is a proof that Rav Hamnuna is not only discussing the Mishnah.

Kol Tuv, and Besoros Tovos,

Dovid Bloom