Unfortunately, I'm not a native German speaker. So, take this with a grain of salt.

I will say that the German language has always been open to loan words from other languages. And, according to my German teacher (who is native), the biggest change recently in that regard is NOT how loan words are accepted BUT how quickly they are accepted these days. New loan words are being added all the time, especially by young people. He said that generally the word will be accepted as it is at first, and then over time it well become more "germanified" and used more like native words. He said this process used to take decades but now it can happen in less than a year. An example of a germanified English loan word is "chatten" which means "to chat," just like English. Ich chatte, du chattest, wir chatten. (I chat, you chat, we chat.)

I believe the simplification of grammatical structures (like the abandonment of genetive) has been going on slowly over centuries and is mostly unrelated to contact with English speakers. But, there is likely some influence there.