My question is, why prostitute does not include in the prohibited
person? Does it mean having sex with prostitute does not considered
Based on its definition, the 3rd precept is obviously a teaching about social (rather than personal) morality. Its essence is to not have sex in a way that harms existing relationships or reputations.
Therefore, to not have sex with those living under the protection of their family is to avoid harming the family relationship or to not have sex with those living in institutions is to avoid harming the social reputation of the institution.
That is why, even today, to have sex in the workplace is generally prohibited by employers & corporations.
That said, having sex with prostitutes falls under the Six Roads That Can Ruin A Man, found in the Sigalovada Sutta
Second question is, from my understanding for married people having
sex with their partner is not an offense but how about having oral sex
or sodomy with your own wife or husband? Is it true that oral sex and
sodomy will make you take rebirth as an animal?
For most worldly people, sex is a necessity. For me, 'rebirth' is a metaphor & rebirth as an 'animal' means to develop the mental state of lacking reason (reflective intelligence) & emotional self-control, just as animals cannot reflect with objective intelligence or control their emotions.
In my opinion, sodomy is 'rebirth' as an animal (i.e., stupidity) since sodomy can be a dangerous activity (since the anus & intestines are not physically designed for sexual activity).
Also, often, women do not actually enjoy anal sex but do it to please the voyeuristic wants of their male partners. At least in past generations, before the era of universal birth control, many women in certain cultures abhorred being forced to have anal sex to satisfy their husbands & avoid pregnancy.
When a man forces or coerces his wife to do an act she really does not want to do, this is 'animal' behaviour & thus 'rebirth' as an animal.
In Buddhism, 'death' is not a requirement for taking 'birth' as an animal, as shown below:
Bhikkhus, these two bright principles protect the world. What are the two? Shame and fear of wrongdoing. If, bhikkhus, these two bright
principles did not protect the world, there would not be discerned
respect for mother or maternal aunt or maternal uncle's wife or a
teacher's wife or the wives of other honored persons, and the world
would have fallen into promiscuity, as with goats, sheep, chickens,
pigs, dogs, and jackals. But as these two bright principles protect
the world, there is discerned respect for mother... and the wives of
other honored persons."
Lokapala Sutta: The Bright Protectors
In the history of Buddhism, some 'authorised Buddhist teachers' (for example, Chögyam Trungpa & his authorised heir Ösel Tendzin) often took 'birth' in this world as 'animals', as demonstrated by their sexual & other social behaviours. For example, Ösel Tendzin had unprotected sex with students while knowing he had AIDS.
Any Buddhist teacher that has sexual relations with a student transgresses the 3rd precept & is immediately ('opapatika') reborn as an 'animal'.
In summary, to preach immorality & to engage in immorality is also 'spontaneous birth' ('opapatika') as an 'animal', even for so-called 'authorised Buddhist teachers'.