Traditionally, children at school (including sixth-form college) are pupils, while students are in post-school education.
headteachers: This is a modern usage but it is fine to say headmaster or headmistress if you know which it is. Some public schools have their own traditional names for the head. These include St Paul’s School, which has a High Master; St Paul’s Girls’ (note apostrophes), which has a High Mistress, and Wellington College, which has a Master. In all cases you can explain it with (headmaster) or (headmistress).
public school should technically be used only for about 250 schools whose heads are members of the Headmasters’ and Headmistresses’ Conference (abbreviated to HMC). You can find a list on www.hmc.org.uk. Other non-state schools may be referred to as ‘private’, ‘fee-paying’ or ‘independent’.
school subjects: All lower case apart from English and other languages.
school years etc: Lower case wherever possible, eg year one, year two, key stage one, national curriculum.
Haberdashers’ Aske’s School: Many Haberdashers, one Mr Aske.
degree classes: These are probably clearer for the layman if spelled out in full, eg upper second (l/c) rather than 2.1 or 2:1. You can say ‘She achieved a first-class degree’, ‘She took a lower second at Hull’ or ‘He took a first at Oxford’. Note that ‘graduate’ (noun) means someone who has a university degree, so you do not need to say ‘a university graduate’.
Johns Hopkins University, Baltimore
London University has recently been reorganised, and Imperial College London (no comma) is now a separate university.
Some of the constituent colleges of London University are King’s College London (no comma), UCL, which was formerly called University College, London (I think you would usually have to say that it is in London), and the London School of Economics and Political Science, normally called the London School of Economics in the first reference and LSE subsequently.
Some other colleges which are still part of London University have adopted the style ‘X, University of London’. These include Birkbeck, Goldsmiths (note: no apostrophe), Queen Mary, St George’s and Royal Holloway. Thus: Goldsmiths, University of London. Other colleges are the London School of Hygiene and Tropical Medicine, the London Business School and the School of Oriental and African Studies.
MA: In most universities this is a further degree requiring study and examination. However holders of Oxford and Cambridge BA degrees may simply apply to become an MA a certain period after graduating. At some Scottish universities the first degree is called an MA.
Oxford and Cambridge colleges: Queens’ College, Cambridge/Queen’s College, Oxford; Magdalene College, Cambridge/Magdalen College, Oxford; St Catharine's College, Cambridge/St Catherine's College, Oxford. All Souls College, Oxford, has no apostrophe (its full name is College of All Souls of the Faithful Departed).
Peninsula Medical School, Plymouth, not Peninsular
Professor: I prefer this in full at every reference, not Prof; the professor (l/c)