In what case is a beast that was mated based on one witness permitted even for the altar?
In halacha 2 it is said that if there is one witness and the owner denies — the animal is permitted even for the altar; in silence, it is specifically forbidden for the altar.
Question 2
What is the main difference between mukzeh and avodah zarah regarding objects on the animal?
In halacha 6: in avodah zarah, the animal and all on it are forbidden for the altar; in mukzeh, the animal is forbidden but the things on it are permitted.
Question 3
What gift is considered 'the hire of a harlot' according to Rambam in laws 8-9?
In halacha 9 it is established that when a man marries a woman forbidden to him by a prohibition, what he gives her for intercourse is the hire and forbidden for the altar; the other three options were permitted there.
Question 4
What is the ruling on a hire given as money, and the woman bought a sacrifice with it?
In halacha 14 it is explained that only the body of the thing given as hire is forbidden; if money was given and a sacrifice was bought with it — the sacrifice is valid.
Question 5
When part of it is shared: one received nine lambs and a dog, and the other ten lambs — when will all ten be forbidden?
In halacha 17: if there is no lamb worth the dog, and every lamb is worth less than it — it turns out that each one includes part of the price of the dog and therefore all are forbidden.