Australian investment abroad refers to Australians placing investments in overseas nations. This is a debit in the capital and financial account (since funds are leaving the country), and means that Australian investors either lent money overseas (debt investment) or bought a stake in a foreign company (equity investment). They 'own' something, they have not 'given it away.'
Foreign exchange turnover is simply the total value of currency that has been swapped in a given foreign exchange market for a given amount of time. For example, if average daily turnover is $180 billion, it means on average $180b worth of currencies are converted to other currencies each day.