Is this still common in British English to use the modal 'shall' with a third person pronoun? If so, what is the difference between the following?
He shall repent.
He should repent.
I shall / he will is, I think, still common amongst older people who were taught a more formal style of English. I use it myself (and it is my natural register) but when teaching English to speakers of other languages we (the tutors and helpers in classes) only teach and use will. Fewer people would naturally use the corresponding I will / he shall form to show determination.
Oxford Dictionaries say:
In practice, though, the two words are used more or less interchangeably, and this is now an acceptable part of standard British and American English; however, the word shall is now seldom used in any normal context in American English.
Most British English speakers would be unable to explain the difference between
The word "shall" is used much less often than "will" in modern English, with some notable exceptions. You should use "will" in almost all contexts.
Religious speeches, text, and pronouncements tend to use "shall" or "shalt", especially in parodies. "He shall repent" is an example of this. Commands from God (such as the Ten Commandments) will almost always use "shall" instead of "will".
Another notable exception is the line "You shall not pass!", which is a reference to Lord of the Rings.
Using shall instead of will in the first sentence expresses certainty (he will certainly repent).
The British traditionally use shall to express determination or intention on the part of the speaker or someone other than the subject of the verb.
He should repent is a supposition that he repents, ought to repent or will repent (depending on context).