No apologies are necessary for the confusion – it is confusing!
I’ve linked to a couple of Point Hacks articles below which will answer some of your questions, and forgive me if I miss anything. But in a nutshell…
If you’re booking Velocity Reward seats, it’ll cost you 139,000 points per person, one way, to fly to Europe in Business class (plus fees and taxes). So, doing the sums, to fly four people in business class (assuming your kids aren’t under 2 years old) to Europe and back will cost 1,112,000 points. I have to say that it will be very difficult to find four Business reward seats on any flight to/from Australia, and you might want to consider splitting yourselves so you’re only looking for 2 reward seats on each flight.
Yes, I have recently (ish) booked Business reward flights to Europe and back, using Velocity points, on Qatar Airlines. I did it by being up at 12am AEST, 330 days before the flights I wanted, when the reward seats were released. Certainly at the time I booked (late last year), more often than not the reward seats were taken by breakfast. So be prepared for some late nights if you want those flights…
When you see that “the going rate” is 240,000 points each way, you’re looking at the number of points required when you use points to pay the fees and taxes. If you pay those carrier charges with money, the number of points required should be 139,000 points.
When you use Velocity points to fly to/from Europe, your main options are Singapore Airlines, Qatar Airways, and Etihad (for some routes you could also go via USA on United). The number of points required is the same (139,000), but the carrier charges are very different. Singapore Airlines’ carrier charges are cheaper than Qatar and Etihad.
You will need fewer points if you do not break the trip up and instead fly direct to Europe (via either Singapore, Doha or Abu Dhabi, depending on the airline).
See the article below for advice on whether it’s worth transferring to KrisFlyer.
I hope this helps!