Yes, you have understood this expression correctly. 'What I wouldn't give for .....!' means I would give absolutely anything to have this. I'd give all my money and sell all my worldly possessions if only I could have this. I can understand your confusion about the structure. The reason this sentence doesn't seem to make sense is that it is unfinished. Many common exclamations are actually unfinished sentences. For example, what we say 'What a lovely house!' this sentence doesn't make sense grammatically, does it? The full sentence is actually 'What a lovely house you have!' or 'What a lovely house this is!', but we only say the first part. 'What I wouldn't give for......!' is similar. It's an exclamation, and exclamations don't have to make grammatical sense in themselves. Like 'What a ...!', the expression 'What I wouldn't give for....!' is an unfinished sentence. So how does it end? In a way, it's not important. Depending on the situation, you could finish the sentence by saying '.......could be written on a postage stamp.' or anything else to mean 'almost nothing' or 'nothing at all'. It doesn't matter how the sentence ends. As with 'What a lovely house!', we don't need to finish the sentence - all that matters is the opinion and the emotion.

This idiom is never used without the "what" at the beginning. Your first sentence is a typo or error of some kind. It is another way of saying "I would give anything for ___". I agree with you, it is not the most beautiful English syntax.