What is 'the/a short end of the deal'? --
the disadvantageous side.
Does this date expression 7/5 mean 7th of May? -- Or the 5th of July. No matter what any style guide tells you, there will always be confused readers if you use numerals only. Spell out (or abbreviate) the month in letters.
Is there any difference in British English and American English?-- Yes, plenty– but little of it of much importance except a few stray vocabulary items like elevator/lift and apartment/flat.