1) We learn from Tosfos Shabbos 42b DH Aval that the parameters are similar. Tosfos writes in the name of Rabeinu Shmuel that since we pasken in our sugya that Tata'ah Gavar, it follows that iruy from a kli rishon has a din of kli sheni. According to Rabeinu Shmuel anything which is permitted to cook in a kil sheni, is also permitted to pour on it from a kil rishon. Tosfos then cites RI who disagrees and maintains that iruy from a kli rishon is not like a kli rishon, and not like kli sheni either. This is because the Halacha follows Shmuel in our sugya; that Tata'ah Gavar; because there is a braisa that supports him here. However, since the braisa states that if one pours hot on top of cold; that one must peel off the top part of the cold item; this proves that iruy does cook a small part of the item, as large as a klipa; so this is worse than a kli sheni. The Shulchan Aruch Orach Chaim 318:10 writes that one may not pour on spices from a kli rishon and the Mishneh Berurah #74 adds that the iruy from the kli rishon cooks a kedei klipah and is forbidden even bedieved.

2) It seems to me that one cannot give the oil of Terumah to a Kohen when it is on the meat, because the Gemara above 32b states that there is no Nesinah to a Kohen if this is less than a Perutah. Tosfos 32b DH veAin writes that one requires a Nesina Chashuvah; it must be an important gift to the Kohen. If the oil was smeared on the meat for a Yisroel, this would not be considered an honourable gift to present to a Kohen.

KOL TUV

Dovid Bloom

Follow-up reply:

3) It seems to me that the reason there is no problem of chometz when the oil drips onto the flour is because the Gemara above top 35b states that "Mai Peiros" do not make chometz. Tosfos there DH uMei writes that this includes oil. He cites Rabeinu Tam that if the Mai Peiros do not contain any water they do not make chometz at all.

Behatzlochah Rabah

Dovid Bloom