So when QE is used (or something similar that results in printing mone), where does the newly created money go? Does some entity get free money? Why is that allowed?
[...] where does the newly created money go?
This money is used by central banks to "buy" commercial banks' bonds $\iff$ commercial banks are refinancing themselves $\iff$ this money goes to commercial banks.
Does some entity get free money?
Yes, when central banks buy commercial banks' bonds for free, i.e. at a 0 interest rate.
Why is that allowed?
The main reason is that as counter-cyclical agents, central banks have to change reference rates to stimulate their national economies, even if sometimes doing so implies to center them on 0, or even on a negative value. Note that in the case of negative interest rates, we are talking about entities that are paid to get money.
E.g. when refinancing themselves at a lower-than-previously cost, commercial banks are theoretically more prompt to be, say, flexible, and thus to stimulate demands (here and there) in the national economy by lending money (here and there). If supplies stay constant, markets will reach a new equilibrium via prices rising (inflation) due to these stimulated demands. Persistent inflation means new business opportunities, which in turn means growth if capacities to cut these opportunities exist domestically, or thanks to foreign direct investments.