1. Rav Ashi's pshat in eruv tavshilin seems strange. Why make a whole new din requiring an eruv to cook from yt to shabbos just so people will make a kol shekain for chol, why not just say the din is you can't cook from yt to chol.And if we're concerned people won't listen, why will they listen to this kol shekain? And if we're concerned people just won't realize it's assur to cook for chol, where do we find such a concern by any other issurim, that people just won't know the din.
Also, the kal v'chomer seems to violate the principle of dayo. But maybe we can say in hachi nami, it's not a real kal vachomer, but lemaaseh people will say it.
2. According to Rava, eruv tavshilin seems to just be a reminder to leave some of the food from YOM Tov over for shabbos. But what does that have to do with cooking on YT for shabbos? If cooking from YT to shabbos is assur, for whatever reason, why should the eruv matir it? And if cooking is not assur, then let it be mutar even without an eruv. Beshlama acc to Rav ashi, the whole point is that you cant cook unless you make the eruv.ut acc to Rava, the eruv seems to be unrelated to cooking.
I also want to clarify: The issur to cook from YT to shabbos was instituted simultaneously with the requirement of eruv, that is, the Chachamim said you cant cook without an eruv. This seems to be the case according to Rav Ashi, is it also true acc to Rava?
Yaron barach, Brooklyn, NY
Rava and Rav Ashi are not explaining why it is permitted to cook from Yom Tov to Shabbos because of an Eiruv. They are explaining why the Eiruv is used to signify this leniency of Chazal. The discussion regarding why Eiruv Tavshilin permits cooking on Yom Tov for Shabbos is an argument between Rabah and Rav Chisda in Pesachim (46b). (See the Gemara there for the answer to your second questions as well.)
All the best,