Upvote:1
You should be fine. You are entering within the validity of your visa, and can do so anywhere in the Schengen area:
Can I visit other Schengen countries on a long-term Schengen visa or residency permit?
As far as your residence permit application, just show the paper to the border guard at your port of entry into the Schengen area. They will likely not need it but have it with you. They will also be able to see in their system (SIS or VIS) that you have a pending residence permit application. Out of sheer curiosity I requested the information in those systems from my current country of residence and found both the issued residence permit info and the residence permit application. See below, "aufenthaltstitel anfrage" = residence permit application.