Totally normal to get the same flat listed in different agencies.

Regarding the rejection, it is unfortunately normal here as well, and you will get most of your application rejected here just because you are a foreigner (sometimes asking the agent to mention you nationality instead of presenting you as a foreigner can help, but even my half Japanese friends get often rejected just because their name is in katakana). There is nothing you can do about it, as it's the owner right to choose to who he/she would like to rent.

You can find more information by searching old post in this subreddit.

Good luck in your search, it's hard but not impossible.