Ophthalmoplegia is the correct spelling applicable in the UK.
The term ophthalmoparesis may be used for the same condition, the weakness or paralysis of eye motor muscles.
That is correct.
That is the correct UK spelling, apologise with an S.But in the US, the correct spelling is apologize, with a Z.(There are a number of similar words spelled differently in UK and US usage.)
The correct spelling is encyclopedia (reference book or work).
That is the correct spelling of the noun apology (an expression of remorse or regret).
That is the correct US spelling of "motorized." The UK variant is motorised.
The correct spelling in British English (UK, Australia, etc) is advertised.The correct spelling in American is advertized.
The correct spelling in British English (UK, Australia, etc) ishaemorrhaging.The correct spelling in American ishemorrhaging.
Specialise is how you would spell that it in the United Kingdom.
The correct US spelling is socializing. (UK socialising)
The spelling colouring is correct in the UK and some other countries.The correct US spelling is coloring.
In British English (UK, Australia, etc) the correct spelling isalphabetise.In American, the spelling isalphabetize.
The correct US spelling is "analyzing" (studying, testing). The UK spelling is analysing.