answers below

Summary
Differences between British and American styles of spelling:
- are small in number.
- have little to do with dialect differences in pronunciation.
- are not consistently followed in either the UK or the USA.
- mostly affect selected words.
- are to do with <-our> versus <-or>, <-re> versus <-er>, consonant doubling, <-ce> versus <-se>, <-ise> versus <-ize>, <ae>/<oe/ versus <e>/<o>.
- can mostly be traced to spelling reform by Noah Webster or the National Education Association.

Which country does this come from? Answer at end

'… the differences between American and, say British English spelling are quite modest' (Cummings, 1988, 26)
'Although American customs in spelling have never differed widely from British, such differences as have existed have nevertheless been treated as though they were matters of some moment, as though the Americans had really done something startling to spelling' (Krapp, 1960, 328)
'All that can be safely asserted of the contemporary conventions of standard Canadian English spelling, when there is a British/American choice, is that the norm is not yet to choose either indifferently for the same word in the same text' (Pratt, 1993, 59)
The Australian Government Style Manual 'arbitrates on many of the currently variable points of English spelling, generally adhering to what is often thought of as British rather than American practice' (Peters & Delbridge, 1989, 129)
'You'll find a cat today must be a hepster. Don't mind if you don't find the word in Webster. He's as square as a bear' (lyric to 'Are You Livin’, Old Man?', Evans, Higginbotham, Silver, 1945)

answers to task 1

The 'University Theatres' sign comes from Madison, Wisconson, USA, showing apparently the trend to revert to British-style 're' in 'centre' and 'theatre'

Short article: Can they spell your name in Karachi?