Your Princess sign in on the website is the same as the Princess App that you downloaded.
I’m surprised that you can’t book shared tables with the DMW. You may want to look at that again.
I’ve booked individual DMW for each night and the whole cruise. Makes no difference. I have found each ship operates a little differently for seating in the MDR’s.
Book the time and MDR that you prefer and shared, if you can. If you can’t booked shared, recheck that. It may change or not be updated yet. If you can’t get shared, then upon arrival on the first evening, speak to the DR manager, tell them you prefer shared and they can change it in the system. However, if you dine with a group the first night, if they agree, you can all ask to be seated at the same table every night. Some ships will do it, others, not as easy.
I’m glad you finally took the plunge! It’s actually a great App, just took a long time to improve and update. The designing stage was lengthy! 😁