Counting the ballots and the preference distribution is by hand. Having scrutineered booths for my party the last 5 or 6 federal elections and many state elections in two states I've some familiarity with it. There are also some details you've got slightly wrong.
- just make a "1". well that doesn't work where preference distribution is compulsory (e.g. federal elections). in that situation you must number all the squares (bar one) starting at your first preference and decreasing order of preference. So a ballot with three candidates and just one marked "1" is an informal vote in that case. Only in some state elections, and council elections, is voting optional preferential (i.e. where you can "exhaust your preferences").
- naturally the number of marked ballots is tallied with the number of marked voters, before the votes are even counted. after the votes are counted, the numbers are again tallied. in fact this often takes the longer than actually just counting the votes.
- Registration. There are certainly flaws with electoral registration in Australia. Howard's mob made some last minute measures just before they were thrashed in the last election in this regard many of which served to disenfranchise sections of the electorate. Generally however these is little registration fraud.
- If you vote multiple times, you will be caught, because the AEC checks for it (they can obviously tell if you've been marked on the roll in several different booths!). And they use a machine to check who has been marked off (have a gander at the way the worker marks the roll next time, it's made for machine reading).
But then I'd say problems with the registration system are quite distinct from problems with the ballot.
Speaking as a party member & voting scrutineer, we are not allowed to touch the ballot boxes or the ballots and can only watch the process occur. I find it totally ludicrous that in the USA party-political hacks are allowed to organise and run the vote! No wonder you get the "Florida situation". The USA needs to get the voting system out of the hands of the people who compete in the elections as its first priority.