I have long been installing mine exactly the way this guy installs the E string at the end of this video. Especially important with round cores.
As for used strings -- why not? The "biohazard" argument is refuted by one alcohol wipe. Except for the homemade bass in my avatar, my basses currently sport "used" strings.
Many times, new strings are changed for reasons other than being worn out. If you want to try and compare a number of different string brands or gauges, it's much less expensive than buying new.
And if you did buy new to compare, or just to use while still nearly new, why not sell the lightly used ones? I have done this, and hopefully it worked out well for the buyer, not just for me.
Admittedly, I would NOT resell strings that I bought used and then played. And I think used flats are far better to re-use than rounds.
I don't like how he wraps initially instead of winding. That will usually put a twist in the string that can give some weird overtones.