As far as I can remember we don't actually learn most of that stuff in corporations law, you might have been better off posting this in the commerce forums.
Company limited by guarantee: You are correct. This kind of company does not have share capital and the members are not required to contribute capital while the company is in operation.
Not sure what you mean by example but most charitable and not-for-profit companies will be registered as public companies limited by guarantee. My notes also say that some sporting clubs will be registered as such as well - I guess those "old boys" golf clubs will often be full of rich people willing to guarantee the club in case it fails?
Unlimited company: Say the company has 10 shareholders. It has $1 million of assets and $11 million debt. It is wound up, after liquidating all of its assets it has $10 million debt remaining. Each shareholder is liable for $1 million.
Say the same company has $1 million of assets but only $1.5 million debt. It is wound up and after all assets are liquidated still owed $500k to creditors. Each shareholder is liable for $50k.
No liability: yep only for mining companies (and only exists in Australia) for policy reasons - mining companies generally have more difficulty in raising funds through issuing shares because a lot of mining activity is very speculative and so shareholders were less willing to invest, or did so under false names so they wouldn't be potentially liable if some mining venture turned out to be a flop because there were actually no minerals in that area or whatever. This is why Parliament created the no liability category so as to encourage shareholders to actually invest in mining companies.