"You have yet to address the fact that the exhibit claimed the Iceman could have fashioned the tools himself. In fact you earlier claimed that that section somehow said nothing about how the tools were made, only how they were maintained. Again you're making interpretations of statements that do not correspond to the actual statements. It just seems like whatever is said you'll interpret as proof that you are correct."
Because it didn't say that, because if it had said that, it would poor scholarship on their part, and likely wrong.
Let us begin with the ax. The ax is cast in copper, to make an ax out of copper one requires a number of things, Ore, Fire hot enough to smelt the ore (a campfire can't do that you need a fire of >200C), A mould in which to pour the molten copper, or a method of collection such that the copper could later be reheated and beaten into shape. Now, Otzi as he was found did not have any of the things required to produce the Ax. (Except perhaps a tool to beat the copper into shape). This means he either had those tools at some point, or acquired the tool from someone else, by means of trade (a market place)
Now let us pretend that Otzi did have these tools at some point and left them behind. There are two more pieces of evidence which suggest he must have traded.
Bread, the remnants of wheat and worn teeth in a pattern indicative of bread consumption were found with Otzi. If we assume that Otzi did in fact act as prospector, finding metal ore, he would not be in a position to farm for grain, farming for grain requires an incredible amount of work to tend the land during the growing season.
Finally Otzi's shoes were produced from bearskin and woven grasses. Weaving grasses is an incredible time consuming activity, making shoes similar to his by hand takes 100s of hours, during that time he also had to kill and skin a bear. While farming and prospecting, and smelting and making tools.
Even if you believe he could accomplish more than one of the roles needed to produce all of these goods. (Plus the many others, including clothes made from cowhide and deer). A more probable and simpler explanation as per occam's razor is that he traded for these supplies, from others who performed specialized functions, such as hunting, farming, herding or prospecting.
Regarding the distance, I will have to try and find the original source. As my present source is notes I had taken on the subject.