I have an MSc degree in natural science and I am currently looking for a PhD position. I saw an advertisement on a researcher community site that an institute at a German university is hiring PhD candidates, where research I am interested in is conducted. I have heard that, at German universities, it is strongly encouraged to contact a potential supervisor before the application, although there could be some exceptional cases. So first, I mailed to the institute director to know whether the professor I want to study with is hiring through this advert.
The director said yes, so I directly sent a mail to the potential supervisor with my CV and my motivation for PhD (about a half page, not a motivation letter, just to show my inclination). I asked if he had any interest in my idea and if he had any kind of comment for me if possible. However, he didn't send any kind of answer to me even after two weeks, so I resent the mail as a reminder. He still didn't answer after another two weeks. I tried to contact him relatively close to the deadline, so I applied without trying any further contact with the potential supervisor. The application was made by sending an email to the institute. Now I would like to know if I have any chance of acceptance. So here are my questions:
Is it okay to apply for a PhD at a German university, even if I could not have any contact with a potential supervisor? I have already contacted some professors at other German universities. In most cases, they sent me an answer, even if they do not have any position, so I am a bit worried if the potential supervisor has even glimpsed my mail.
Plus, if the professor read my email but didn't reply, could this be a negative sign, i.e., the potential supervisor didn't like my idea so didn't reply to me back? I know that in some US universities, it is prohibited that the professor responds to students' mail before admission to establish fairness. But I have no idea whether this might be the same for some German universities.
As it is the first time for me to apply only through emails, I am wondering how the process is handled. How many weeks should I wait to know if I have a chance for an interview in general, especially for this kind of application process? I have no idea when they announce the result. Or may I ask the office at the institute directly? They would surely have many applications and be busy, so I don't want to irritate them if possible.