1) [line 9] V'CHI REBBI LO SHENA'AH, REBBI CHIYA MINAYIN LO? - since Rebbi
did not teach it in the Mishnah (because he did not want to establish the
Halachah accordingly), then from where did Rebbi Chiya, his student,
conclude that it is the Halachah?!
Here, undoubtedly, this is meant as a refutation of this tradition in the name of Rabbi Chiya; however I seem to remember that this phrase is sometimes used quite the other way: as a support for something said by Rabbi Chiya, implying that his statement is authoritative!
Is this an example of strange usages in Eruvin?
The usage of this phrase here is similar to the other places that the Gemara uses such a phrase (Nidah 62b, Yevamos 43b, see also Beitzah 6b, RASHI DH v'Chi Teima), and it means to refute the statement said in the name of Rebbi Chiya.