Can impure food (a secondary derivative) impart impurity to a vessel it touches?
Halacha 1: the Sages decreed that impure food imparts impurity to other food and to liquids, but food never imparts impurity to vessels — even Rabbinically.
Question 2
Wine touches a primary source of impurity. That wine then touches oil, oil touches milk, milk touches honey — what is honey's status?
Halacha 5: impure liquids are always primary (techilah) — they impart to other liquids which in turn remain primary. There is no concept of 2nd/3rd degree for liquids in this chain.
Question 3
Impure liquids touch the OUTER surface of a terumah vessel. What is the status of foods inside that vessel?
Halacha 6: when only the outer surface of a vessel becomes impure, food inside it remains pure for terumah. Only for kodesh (consecrated food) does the outer impurity spread throughout the vessel.
Question 4
Why did the Sages create the rule that outer-surface vessel impurity doesn't spread to the inside for terumah?
Halacha 4: the Sages made this distinction specifically to publicize that liquid-to-vessel impurity is Rabbinic — so people would not burn terumah or kodesh based on this impurity.
Question 5
Liquid A touched a secondary derivative of impurity (2nd degree person). What is liquid A's status?
Halacha 5: even if a liquid touched a secondary derivative (person or vessel), it is still considered primary (techilah) — impure liquids are always primary and transmit onward as primary.