Question 1: Yes, that's correct. Only Qantas operated flights with a QF flight number qualify for upgrades.
Question 2: The problem is that you've missed the boat most likely as you're well within the booking window and most reward seats have been gobbled up already. Now, there may yet be more released, but unlikely unfortunately. Also popular routes like SYD-BKK are extra hard (SYD-HNL is another notorious one for example). I'm not saying it's impossible, but it's going to be difficult.
You might, if you have not already tried, to use the multi-city tool and break down what you want. You have an idea with Singapore, and potentially either redeem a jetstar asia Y reward to BKK (or just buy seats on any number of carriers from SIN)
As for europe - 1. London to fly out of will kill you with the APD (tax) on premium tickets, and also is very popular. I would look for reward flights to or through AMS on KLM as an option, and to other cities. If London is really wanted, look at DXB-LGW (Gatwick) on EK, or to MAN, or say somplace like BRU (see if there's any F seats on the "game changer"!) or other nearby locations in europe you could then train (or fly cheap) from to Paris or London.
You may need to be creative, and consider going via CMB (SriLankan), AMM(RJ) or HEL (AY).
another option is to get a paid JQ fare to SIN/BKK and look to rewards from there on say CX/MH/EK/KL etc) to europe.
good luck!