Welcome to the forum, you should get all the answers you need here. I am not too far away from you up at Lindfield near Middle Harbour. I am a member of the North Shore Beekeepers and Northern Beaches Branch of the ABA (not sure if you are a member of these) they are an excellent club with regular talks, courses and field days.
I can probably help with the Small Hive Beetle issue. I recommend oil in the tray and replace it weekly to prevent it going rancid on you, especially after heavy rain. Another alternative is Diathomaceous Earth which also needs to be replaced regularly. I also use a folded chux cloth on top of the super on a mat (as the bees like to try and pull it down between the frames to get it out of the hive. For 5-6 beetles you don’t have a major issue there but do squish as many as you can, especially while your colony is young.
I also have chickens but no longer recommend allowing them near the hives after losing 2 of them to bee stings. Oil in your tray will do the trick with the majority of the grubs falling through the screen.
Autumn in Sydney is when the melaleuca’s and banksia’s come into flower, winter is scribblygum and stringybark if there are street plantings near you. I find the Sydney based colonies don’t require any feeding and if you do feed then chances are it will end up in your honey and you’ll miss all the benefits as the bees won’t need to collect from the trees. Just give them time to build, you’ll be surprised how quickly this occurs if you have a productive worker colony and queen.