I recently applied for a PhD position in Europe. The deadline for applications was the 30th of September (so almost a week ago) and the starting date for the position is January 2021. I won't graduate until June 2021, but nevertheless, I decided to send my application since I'm really interested in the position. After sending my application (3 weeks ago), I contacted the professor with the question if it's possible to start later, after graduation, and he told me that they need to discuss this and that I could apply.
I would like to send an email to ask if they already decided if it's possible to delay the starting date and to ask when I can expect to hear back from my application (there is little information about the admission procedure on the website). I don't want to be pushy, but I really want to show that I'm really motivated. Should I send an email or should I just wait until I hear back from them? How long should I wait?