Can a Bhikkhu yell at or beat a lay person under the vinaya?

Even torward a cat, insects or non-human, neither insulting nor even beating would be proper and allowable, in cases against humans it might be even seens as heavier then toward a fellow or novice.

It falls like many other things (really and by far, not all has been caught in special wording or rules) under that what is called derived offenses, some are mentioned in commentary or sub-c. or "just" to figure out at times, using the great standard:

"Bhikkhus, whatever I have not objected to, saying, 'This is not allowable,' if it conforms with what is not allowable, if it goes against [literally, "preempts"] what is allowable, that is not allowable for you.

"Whatever I have not objected to, saying, 'This is not allowable,' if it conforms with what is allowable, if it goes against what is not allowable, that is allowable for you.

"And whatever I have not permitted, saying, 'This is allowable,' if it conforms with what is not allowable, if it goes against what is allowable, that is not allowable for you.

"And whatever I have not permitted, saying, 'This is allowable,' if it conforms with what is allowable, if it goes against what is not allowable, that is allowable for you." — Mv.VI.40.1

Something actually very hard for those not tending to higher virtue.

The BMC1 tells about Pc2:

To insult a bhikkhu incurs a pācittiya; to insult an unordained person — according to the Commentary, this runs the gamut from bhikkhunīs to all other living beings — a dukkaṭa.

For example. My person would not agree, since generally "foreign-policy agenda" are generally given more sensibility. If we take the cases in BMC2 in relation with lay people it allows the Sangha to take on disciplinary measures.

See Reconciliation BMC2 and the story of Cv.I.18.1-5

The Community, if it wants to, may impose a reconciliation transaction on a bhikkhu endowed with any of the following qualities:

a) he strives for the material loss of householders, for the detriment of householders, for the non-residence of householders (so they can't live in a certain place); he insults and reviles householders; he gets householders to break with householders;

b) he speaks in dispraise of the Buddha to householders, speaks in dispraise of the Dhamma to householders, speaks in dispraise of the Saṅgha to householders, ridicules and scoffs at householders about something low or vile, does not fulfill a righteous promise made to householders [C: this includes accepting an invitation for the Rains retreat or any other similar promise].

Generally in regard of the basic precepts, not to speak about kammic effects, there is no exclusion for Bhikkhus at all and the Vinaya contains aside of "foreign political" and community rules specifical special mentionings of cases where Bhikkhus obiviously had to less objectivity, such as water filter, digging earth... It's importand to understand, that Vinaya rules are for the most cases for very undeveloped minds and wordlings. Whom would one need to tell about issues of being in water, earth or possible endangered by uncontrolled fire... if not someone who is far away from higher virtue and controll of the sense faculties and mind.

How to handle things is always a case to case matter, requiring people with lot of knowledge and understanding of Vinaya so that the right kind of offense class is selected.

So aside of the Patimokkhas 227 rules, 1000 in Mv and Cv and other books, "countless" other cases need to be deriven form the given set and especially today many have of course real problem.

One, like also mentioned in the Suttas, who trains firm in higher virtue, concentration, wisdom, would aside of community and costume rules have no problems at all, sticking firm to the basics and fundamentas precepts.

There are those who argue just in literary ways, even thinking (following the words) that Bhikkhus might have more ease than Samaneras for example, or householder and there are also many cases where householder rules are explained by the Vinaya standards, but that is mostly wrong. Vinaya should be seen as addition to the basics to have common min. standards and not as replacements at all. Again, not to speak of kammic effects, where there is no difference in what ever cloth one might wear.

Hope that this short explaining could ease in the regards of shock displayed in the question.

In cases where a lay person might be really ill willed harmed by a monk it's good and proper, if no backwards need to be feared, to speak out such cases to other trusted monks since it is not good, for anybody, to keep problem, possible also misunderstandings, a burden for good relation. "Sadly" such as "opening the Vihara" is not really broad known and practiced but a good and performed way to clean things up, used here in Cambodia, for example, in the Dhammayut Nikaya. When lay people see grave problems they are given to call for "opening the Vihara" where they then are given to bring up their cases in front of an assembling of monks and possible the involved people. Not that such is a desired and pleasant event, but it is a very good tool for healing and clarify possible misunderstandings as well since it is somehow public.

At least one should not forget that a Bhikkhu is not immune and excluded in regard of criminal law for cases where the Sangha is not really capable to handle cases. Beating and serious ill-willed insult are no trivial offence in most counties. Of course it's better to solve it in amicable arrangement but in certain countries one would be even obligated to legally report it.

If a monk deprives lay people from their possessions and states, advocate such, promote such and tell others to do, if a layperson loses (such as a legal case, right or wrong), he insures a Pārājika, the same also in regard of killing. There are actually many "monks" who, by Vinaya, are no more. Think on certain movements, euthanasia, abortion... hate speech toward not beloved, support of legal actions... So stay away from those and be sure that merits toward those are just for harm in the world and will seldom bear even small fruits. Even association with them or using things from them will have much disadvantages for one, cuts one off from good monks and the Savaka Sangha.

[Note: This is a gift of Dhamma and not meant for commercial purpose or other low wordily gains by means of trade and exchange.]