You must all be living in caves then. It was on the last renewal you must have received. Not that it matters, if your tax runs beyond October 1st you'll be told about the new system when you get your reminder to renew your tax. Taking your bullet points one at a time
It's been mentioned in newspapers, online, on websites and forums (including this one) and, as said, on the last renewal you would have received.
If you buy a bike on a Sunday not only can you not tax it if you don't have online access but the previous keeper can't cancel the tax either so it's still taxed until he tells them he's sold it. It's no different to now, he is still responsible until he tells them he no longer has it, the only difference is that as well as being responsible for speeding and parking tickets, he's responsible for the tax too.
If the system is down the same applies as above, it's still taxed.
Personally I think the new system is much better. No need to display a tax disc, the option to pay monthly by direct debit, the option to cancel the direct debit and declare sorn at any time so if you want to only tax something for a month you can. In other countries that have a road tax, almost all of them have the tax with the owner and not the vehicle just the same as the owner gets the plates issued to him for a particular vehicle and they stay with him when it is sold, they don't stay with the vehicle.