"farthest down" here means "most advanced". It means that, compared with the competition, someone is most knowledgeable in experience curve theory

I found the power point presentation that this came from. It's a lot of business jargon, but the slide you refer to seems to be listing the attributes that extremely successful companies have. I believe they're trying to say that a star company has more experience or has been in business longer than other companies (their competitors).

No. Actually it is a description of the Stars in Boston Consulting Group Matrix. Using a BCG Matrix, the SBUs/products of a firm can be classified into four cell matrix - stars, question marks, cash cows, and dogs.

Is that the entire sentence? I can't make any sense of it.