The securities are a red herring. The Fed trading desk effectively lends or borrows money in the fed funds market to maintain the FFR. These loans are known as Repos (repurchase agreements), because technically they are an agreement to buy and sell back securities at some nominal price. In economic reality, the securities are nothing more than collateral for the loan.
If the Fed uses open market operations to buy/sell securities at market prices (instead of Repos), then that is for the purpose of making permanent changes to the monetary base.
If a US company orders wine in Australia, priced in AUD, then it must first change its USD to AUD on the forex markets.
If the wine company exports wine to the US, and prices it there in USD, then the wine company would then sell its USD earnings for AUD on the forex markets.
The RBA (Reserve Bank of Aust), as far as I remember, is fairly non-interventionist and engages relatively rarely in forex transactions.
Central banks of countries with freely traded currencies tend to trade on forex markets only for the purpose of propping up or lowering the value of the currency.
If a country (say the US) is running a net trade deficit, then some other country must be running a net trade surplus (say AU). That implies that AU will end up with a surplus of USD. But those USD are just sitting in a US bank account which now has an Australian owner. If the Australian owner exchanges it on the forex markets, then the USD will be transferred to a US account owned by the forex dealer.
At any rate, whosever account the surplus USD ends up in will either withdraw it as currency (uncommon), spend it, or invest it (and that includes holding it in the account, since all bank deposits are loans to the bank). If it invests it, e.g. by buying bonds or shares, then that will help keep interest rates low. Massive Asian investment in US bonds has indeed kept USD interest rates low.
Only withdrawal of cash as currency will actually remove money from US banks. The effect of such hoarding would be to increase the demand for USD, which would lower the price of US goods, which would in turn make it more attractive to spend the hoarded USD.
Trade deficits can persist only for as long as the surplus nation is willing to invest its surplus in the deficit nation. The distortion in US world trade at present is due to the Asian mercantilist desire to keep their currencies low. Long term USD interest rates are low, courtesy of the Asian taxpayer.