The Tana does not seem to differentiate between the first and second days of Yom Tov regarding a stolen Lulav.

Question: But the Torah singles out the first day for the obligation that the Lulav belong to the user!?

Answer (R. Yochanan citing R. Shimon b. Yochai): Because on all days it is a Mitzvah ha'Ba'ah b'Aveirah.

Malachi connects the stolen offering with the lame and ill offering.

The defect of being stolen does not abate, just as the lame condition of the animal does not pass, even after the owner loses hope (Yiush).

Question: While before Yiush we understand that the offering does not belong to the one bringing it; surely after Yiush it is his!?

Answer: The invalidation must be Mitzvah ha'Ba'ah b'Aveirah.

In a similar vein R. Shimon b. Yochai interprets the Pasuk wherein Hash-m despises theft in an Olah.

It is analogous to a King who pays taxes (which come right back to him) so that his servants will not learn to evade taxes; so, too, does Hash-m despise a stolen Olah, so that we might learn to avoid theft.

R. Ami teaches explicitly that the defect of a stolen Lulav is Mitzvah ha'Ba'ah b'Aveirah.

(R. Yitzchak citing Shmuel): One does fulfil one's obligation on the second day of Sukos with a stolen Lulav (since a borrowed Lulav may be used, so, too, a stolen Lulav).

Question: But our Mishnah prohibits a stolen Lulav and thus seems to permit a borrowed Lulav!?

This could not be speaking on the first day of Sukos, where the Torah says Lachem (and a borrowed Lulav does not qualify)!

It must be speaking on subsequent days, and, still, a stolen Lulav is Pasul!

Answer (Rava): The Mishnah is speaking on the first day of Yom Tov.

The Mishnah singles out a stolen Lulav not because a borrowed one is permitted.

To the contrary, we would naturally prohibit a borrowed one (which is not Lachem) but we might have permitted a stolen Lulav (by presuming that commonly the owners have lost hope).

R. Huna told the merchants to have the gentile sellers cut the Hadasim (not the merchants).

Question: Why would this be necessary?

Answer: Since the gentile presumably stole the property (perhaps from a Jew).

Since property does not change ownership by theft it may still belong to a Jew.

Having the gentile clip the Hadasim results in the permitted combination of Yiush and change of ownership [Shinui Reshus].

Thus the Yiush takes place in the hands of the gentile, and the Shinui Reshus is into the hands of the merchant.

Question: It should be sufficient that the Yiush takes place as it is clipped by the merchant, and the Shinui Reshus takes place into the hands of the buyer!?

Answer: Indeed, R. Huna was speaking to the merchants about acquiring their own Hadasim from the gentile.

Question: Let Shinui Ma'aseh be sufficient (tying together of the Minim)!?

Answer: R. Huna does not require that they be bound (and even if he does, such a binding does not create Shinui Ma'aseh since it can be readily undone).

Question: Let Shinui Hash-m be sufficient (it was called a Asa [Hadas] and it is now Hoshana)!?

Answer: It was commonly called Hoshana even before it was tied together with the Minim.