The validity date of the visa and the number of days you get are independent of each other.
If your visa is valid until say September 22nd (a made up date) and you enter on the 22nd or anytime before you’d be given a stamp for whatever amount of days you’d be allowed. You mention 60 days so I’m assuming you may have applied for a tourist visa (which for most people is not needed these days - but that’s by the by).
Your visa is correct. It runs from the date of issue. Depending on the visa you applied for that would normally be 90 days from issue.
If you’ve applied too early then that’s on you. You’ll rarely have any luck contacting an embassy but even if you could it wouldn’t change the fact that your visa is correct.
There is no such thing as a 1 month tourist visa. I suspect you’re referring to a 30 day visa exempt stamp that you got. Way back when exempt stamps were 30 days there wasn’t an issue for most opening an account.
In the past few months it’s become almost impossible to do so for anyone not on a long term visa.
Your experience 2 or 3 years ago is irrelevant these days.
Yes it can be done all online in Australia. Indeed it needs to be done in Australia (if that’s where you physically are). Sydney covers those residing in NSW. Canberra covers elsewhere.