it's always 'The Hague', never 'Hague' or 'the Hague'.

and hearty, hail a taxi

not hollowed

people are hanged, pictures hung

'Born in Hobart in 1909, his daughter Rory has now donated her father's memorabilia to the Tasmanian Museum...' That would make Rory 99—not unreasonable except this is the second paragraph of a story about Errol Flynn and his daughter Rory. Much better to repeat the name: Errol Flynn was born in Hobart in 1909, and his daughter Rory has now donated her father's...etc.

The premier took a hard line on the proposed tax. What kind of line? Hard. The minister proposed a hardline policy. What kind of policy? Hardline.

not bailing

'Is Australia heading (not headed) for a hung parliament?' Best to avoid 'headed' here because its use as anything other than the past tense of the verb 'to head' is hard to justify in Australian usage.

please consider using other verbs such as going, travelling, flying. 'Heading to' is overused.

please use newspaper headline style, with the first word capitalised but the rest lower-cased. 'Lebanon update', not 'Lebanon Update'; 'Live concert from Port Fairy', not 'Live Concert from Port Fairy'.

town in Pilbara Region of Western Australia

not hullo or hallo

not Katherine

one word

no capitals, no hyphen

hip-pocket nerve

the fall of the Berlin Wall was a historic event, but most public libraries hold historical documents

'More than one million people died in that famine and now there are fears that history could be repeating.' Propellerheads and Shirley Bassey have made 'history repeating' stick in our brains, but in a serious discussion of world hunger we should write '...history could be repeating itself.'

Human immunodeficiency virus which may lead to AIDS (acquired immune deficiency syndrome)

the masses, the people (it doesn't mean high and mighty, which is hoity-toity

snobbish, haughty

the dance

hocus pocus, or trickery, or brittle toffee in New Zealand

to your sanity

a clamping device

full of holes (holy, holiness is spiritual excellence)

self-righteous

of people ... a hoard of treasure

(singular and plural)

one word

a hotel—and all other words beginning with H where the H is pronounced. So it's a historian, a historic occasion, but an honour, an heir.

the pureé

If you're writing in America you use humor. In Australia it's still definitely humour. But just to be contrary, it's humorist and humorous everywhere.

the rotted vegetation

never after adverbs ending in -ly, as in 'fully financed', 'partly paid' (but part-paid does need one). And be careful where you put hyphens: anti-sexual assault classes might suggest a new kind of martial art. Anti sexual-assault classes has a clearer meaning.