Nice connections, neat box.

Output fuse: in this scenario makes little sense.
Input fuse: depends.
Fuse’s job is to protect your home installation and power cord from overheating, if the device fails. I believe in Australia standard outlets are 10 A. If you used a cord with a lower current rating, choose the fuse with the same value.
(1) Your home already has circuit breakers installed (I hope so!

), so don’t be worried too much. The fuse is only a backup for a very reliable system.
A fuse may also limit the risk of a fire or smoldering inside the device. I used word “limit” intentionally. Yet, of course, may still be worth doing. The minimum value is determined by how much power you wish to draw from that transformer. We still don’t know, how much power it can deliver. Let’s
guess — based on the look of it, what it came from, and voltages used — that it’s 10–20 W top. 20 W / 240 V ≈ 84 mA. So a 100 mA or 250 mA fuse should be fine, given the above guess is correct. Don’t try to match the value exactly: it is going to be too low, while providing no additional protection. This risk is, in your case, minimal: transformers are hard to set on fire.
(citation needed) So, again, don’t be too worried you did something wrong.
I agree with chilternview, that proper strain relief is preferred over a knot. But a knot works better than nothing, so don’t undo it until you can mount a proper stress relief.
The taps indeed seem to be as chilternview described them. How the wires come out of the transformer is in agreement with that. One thing to be aware of is the polarity. Both black-to-blue nad black-to-yellow (note the order!) are 8.4 V, but 180° out of phase.
(1) I don’t know about Australia, but down here we have things like
eurplug. Rated for a fraction of the normal value and in many situations the wiring in the device or in the cord is capable of even less.