'But like many of her female contemporaries *their influence is not fully understood...' Their here is wrong. The comparison with a group does not alter the singular subject. The correct version is But, like many of her female contemporaries, her influence is not fully understood.
When generalising about Australians, some Australians start off in the third person : 'Many Australians...' then switch to first person to include themselves: 'plant native trees in our gardens.' Should be either 'Many Australians plant native trees in their gardens,' or 'Many of us in Australia plant native trees in our gardens.'
'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.
or dangling modifiers, become a problem if a reader has to pause to work out how a sentence should be understood. For example, 'Driving up to the house, her dog always barks loudly.' That split-second hesitation while you work out what's going on can be avoided by writing 'Her dog always barks loudly when she drives up to the house.' We still don't know if the dog's in the car or in the house, but at least it's not driving.
not between you and I
committee, jury, choir, audience: the audience were (plural) drifting in to the auditorium in ones and twos; the entire audience was (singular) on its feet. Use of singular or plural verb depends on how you want the collective noun to be understood.