Punishments for breaking vinaya rules

There are a lot and the topic is very complex: The Buddhist Monastic Code I The Patimokkha Training Rules Translated and Explained

The heavier punishments are found in BMC2 CHAPTER 20: Disciplinary Transactions

"Punishments for breaking vinaya rules" The Dhamma Shown to the world by Lord Buddha and the Vinaya promulgated by Lord Buddha do not prescribe punishments. The sub-questions related to the question do not arise.

A person becomes a Pabbajita by makes a solemn promise by uttering:Buddham Saranam Gacchami, Dhammam Saranam Gacchami, Sangham Saranam Gacchami,three times after his teacher, according to a formal procedure. The procedure is same for Upasampada also.[See Vinaya Mahavagga]

The responsibility for observing the Patimokkha rules rests with the Bhikkhu. If he breaks any of the rules he must purify himself before attending the next Uposatha.

If a dispute between two bhikkhus arise, then there is a procedure called Adhikarana to settle the matter. [Adhikaranasamathasutta AN].

Sukha Sanghassa Samaggi (Lord Buddha)

In theory the Pāṭimokkha Rules: Intro | Bhikkhus' | Bhikkhunis' is the basic code of monastic discipline, consisting of 227 rules for monks (bhikkhus) and 311 for nuns. It lays down offences and punishments leading to a maximum of expulsion from the order. The punishment is typically decided by the Sangha, but the presiding abbot may decide on occasion when it is not feasible to assemble the sangha.

http://www.wisdomlib.org/buddhism/book/buddhist-monastic-discipline/d/doc4046.html

The code of the Pātimokkha itself, in its details of disciplinary procedure, recommends certain forms of penalties for the categories of major offences. The Pārājika, being the gravest of the monastic offences, admits of no remedies or atonements. The penalty for Pārājika offences being complete ex-communication and loss of monastic status, it is spontaneously brought about by the commission of the crime.

All offences other than the Prājika are remediable in that every offender, barring one who is guilty of a Pārājika offence, who submits himself to the specified penalties and punishments and behaves himself in accordance with the law is considered as being purged of his guilt. The Saṇghādisesas include a host of offences for which specified penalties are to be imposed by the Saṇgha, taking into consideration the circumstances attendant on the commission of the crime.

In practice, it appears to vary depending on the monastery/monastic order, the country and the culture - barring the grave offences, there appears to be a lot of leeway in how the offences are viewed.

Some countries like Thailand have in the past got involved in the disciplining of monks because the monastic order itself wasn't doing enough, or because the state was outraged by certain infamous incidents.

While it appears that punishments are generally very rare in most Buddhist countries, Japanese Zen monasteries are famous for offering very tough disciplinary punishments for the smallest of offences, often decided solely by the abbot. So obviously culture has a large role to play in all this.

A strict reading of the Pāṭimokkha would make cooking an offence worthy of confession. However, monks have to adapt to new cultures and times - for example the monks and nuns of the Plum Village order in France under the tradition of Ven. Thich Nhat Hanh do their own cooking and even cook for lay people because it is nearly impossible to go on alms rounds in the countryside where they live.

The Buddha was rather pragmatic about the rules it would appear,

AN 3.83: Vajjiputta Sutta — The Vajjian Monk {A i 230; Thai 3.85} [Thanissaro]. A monk who is having difficulty following all the Pāṭimokkha training rules can boil them all down to these three: the training in heightened virtue, the training in heightened mind, the training in heightened discernment.