Hello Oleander,
Some of the others might have another slant on this, but I think the 'fair' in dinkum comes from being fair about something (balanced, honest, etc). So I guess 'fair dinkum' equates with 'honest injun'.
Similarly, 'fair suck of the sav' (saveloy) or 'fair suck of the sauce bottle' refers to sharing something fairly and equates to 'be fair about it' or 'you've had your say, now let the other person have their turn'. I'm probably sticking my neck out here, but from my own observations, 'fair suck of the sav' seems to be a Victorian term (I first heard Graham Kennedy - who was a well known Vicctorian comedian on tv - say it forty-odd years ago) and 'fair suck of the sauce bottle' a Queensland one. In my early days in New South, we seemed to stick to 'fair go'. (Don't take this as bible, though.)
'fair enough' is used to let the other person know you accept what they have to say as being a logical and accurate description or assessment of a situation or problem.
'fair' does also refer to 'large' at times, as in 'it is a fair way between Sydney and Perth'. (If someone tells you it's a fair hike to somewhere, they are advising you to go by bus or drive rather than walk.)
I have always been fascinated by 'fair cow'.
Last night I watched an animal rescue program, where three RSPCA (same as SPCA except it has Royal patronage) officers were trying to help an aged cow get out of a muddy riverbank. It had been there for days and was exhausted from trying to extricate itself. The men dug under it to get big straps around it and attempted to pull it out of the mud, to no avail. The animal was unable to do anything to help and was a dead weight. Eventually three more men who were working nearby gave them a hand and finally the six of them were able to drag the poor creature free. They then found that the cow was too weak to attempt to stand, let alone climb up the steep embankment to reach safety. So they then got hold of an inflatable dinghy and lashed the cow to the side and 'swam' it along the river until they reached a level area where the animal ambulance could back down to the water's edge and they were able to drag the cow up a ramp into the ambulance. Oh yeah, I forgot to mention, the river was infested with bull sharks.
I thought it epitomised the saying perfectly.
So if something is described as a 'fair cow' you can rest assured it is a seemingly insurmountable and unpleasant problem.
I'm glad you see the fun side of it, because that is the real basis of Aussie slang. Survival for the convicts, early settlers, the bushmen, farmers, and even the city dwellers, has always been a battle against harsh conditions. The best way to cope with this day after day was to show no fear, whistle in the dark, take the mickey out of yourself and each other (ie, laugh). Thus we nickname redheads 'Bluey', bald men 'Curly', morose people 'Chuckles'.
Edit::: I prepared this earlier today, but I had problems with the line and was unable to post it until now. I see a couple of other Aussies have answered as well, so this may seem to be repeating some of what has been said above.
Oh, by the way, if you are so keen on Aussie slang, I DO hope you pronounce it OZZY not Ossy!
