If a wizard sells a second-hand wand, is this the same as winning it in a duel? Could Voldemort have bought the Elder Wand from Snape instead of killing him for it?
I'd hazard a guess at no, it wouldn't count.
Ollivander states that a conquered wand will usually bend.
"I took this wand from Draco Malfoy by force," said Harry. "Can I use it safely?"
"I think so. Subtle laws govern wand ownership, but the conquered wand will usually bend its will to its new master."
Harry Potter and the Deathly Hallows, chapter 24: "The Wandmaker"
And when Harry Potter uses Hermione Granger's blackthorn wand, which she willingly let him use, he has trouble with it.
The spider did not shrink. Harry looked down at the blackthorn wand. Every minor spell he had cast with it so far that day had seemed less powerful than those he had produced with his phoenix wand. The new one felt intrusively unfamiliar, like having somebody else’s hand sewn to the end of his arm.
Harry Potter and the Deathly Hallows, chapter 20: "Xenophilius Lovegood"
Selling a wand would probably also count as willingly given, and not conquered.
No, When Harry first buys a wand he needs to try several before he finds one that is right for him. This is not the case for a captured wand which always belonged to the winner of the wand.