The HAI (hot air intake) mod works, and doesn't...
Bottom line though is that for such small change(s), you perceived change is most likely placebo induced. You aren't really going to "feel" a 10hp difference. You could get that effect from just changing gas supplier (E content).
As for the ECU adjust... I had a conversation with a well established BMW guru, modder, racer at my dealership. We discussed some mods and programming changes, etc. as I've tuned some of my older cars. He assured me, that will most of the physical mods, these ecu's will adjust. Like for the added air with an open cone AND downpipe, or added midpipe / exhaust. This surprised me honestly... My knowledge is that ecu's don't, as they're expecting a certain VE from stock parts. Changes to Air, Fuel, or Spark requires an accommodation in those others to keep the balance and best performance. But hey... I'm old school. Again, you aren't going to feel 10hp difference... Maybe just maybe of you had 2 identical cars sitting side by side and drove one, immediately got out and in the other and drove right away... You might, and that's a huge maybe!
The Burger open cone really is just that, but don't buy into the Manufacturer spends a lot of $ designing the BEST for every single component... It's not true. Air intake otherwise would ALL be from scoups on the front of the hood and not underneath it from a small pickup tube wedged into the side of the heat exchanger/radiator... Sorry! So yeah, you might get a different result from another brand. That's the thing with modding, it's a lot of trial and error to get what YOU want. Sell the one you have, take a 50% hit, it's ok, and buy another
lol
Good luck!