I am going to come for studies in the summer semester, but in the application, I am applying for the winter semester so that they can review it and send the invitation earlier. Later, will I need to write to them to move my invitation to the summer semester? Or how should I do it? Please advise me.
No. The validity period of the invitation will be specified (2 years), and you must arrive in time, complete the preparatory courses for foreigners (German and additional subjects), and enroll in the university. If you apply in advance, it may actually turn out to be 1.5 years, it will be more difficult to manage in time.
Not quite... during the validity period of the invitation, one needs to obtain a residence permit, but the duration of the preparatory courses is 2 years in which all required subjects must be passed... 2 years for the preparatory program and the invitation period can be separated in time.