Why is the Argentine Peso still so expensive? In the last twelve months, the argentine peso (ARS) lost about 11% of its value in comparison to USD.

In the same time range the prices rouse about 29% (spanish).

What's the reason for this effect? I am living in Argentina for about 2 years, and the prices even feel worse to the published statistics. The government is acting very "special": it's starting social programs one after another and is building lots of (unneeded, or at least oversized) infrastructure using money with unclear origin (well, a lot of this money is draining in similar circumstances, too).

So, who is willing to pay this price for Pesos, since they do not have any value outside of argentina? In my expectation the demand for Pesos is really low, and since Argentina maintains a trade deficit, it is forced to import lots of goods, payed with Dollars. They should have a pressing demand for Dollars. And economics say: low demand + great offer = low price.
Buying and selling of currencies in Argentina is currently strongly controlled by the government:
http://www.reuters.com/article/2015/02/09/argentina-imports-idUSL5N0VJ4I520150209

This means that you cannot buy as many Dollars as you want, but the ones you buy you get at a government controlled exchange rate, which is actually cheaper. The Argentine government might have to pay 10 Pesos for a Dollar, but they sell it to the importer for 8 Pesos. They do this so that consumer prices do not spiral out of control. Hence the current exchange rate is not what it would be in an uncontrolled market. Further devaluation (controlled by the government) is expected next year, because this subsidized exchange is too costly for the government:
http://www.bloomberg.com/news/articles/2015-03-18/argentine-peso-forwards-at-record-show-devaluation-bet-for-2016

As for your second question: while the Peso may not have any value outside of Argentina, individuals and firms that buy products in Argentina will still have a use for it. For example a US firm importing and selling Argentine beef will trade Dollars for Pesos.