Answer:
It's to support subject/verb inversion (as in "neither do I" or "so do we"). So 'does' is standing in for the main verb, 'discover' because modern English avoids inverting except with auxiliary verbs such as do, can, will. Without 'does', you'd have to say 'Only by ... views of others DISCOVERS ONE ...' which isn't done in modern English.
Answer:
This sentence:
While hundreds of new hair and beauty products enter the market every year: sometimes the oldest solutions are still the best.
Is incorrect.
Explanation:
The reasons this sentence is incorrect are two. First of all the colon is used incorrectly. Because it is used to provide specific information that falls into a category that is produced by the sentence before the colons. However, in our case we don't only receive an example of that category's elements. But an explanation. And explanations shouldn't be introduced by colons. They should be followed by them, making it very clear the following elements are part of the category presented.
