It is not possible to apply for the 1st semester in the summer semester. Applications for the 1st semester can only be submitted for the winter semester.

However, applications for higher semesters in the summer semester are possible. For the requirements, see https://www.stat.de/archives/ufaqs/can-i-apply-for-higher-study-semesters-hohere-fachsemester .

1. There have to be available studying slots in the higher study semester, which is seldom the case.
2. If you fulfill regular admission requirements and you have completed the necessary creditable courses at the time of application you can apply for a higher study semester. For example, if you want to apply for the 2nd semester in the summer, you need 30 completed ECTS from the Statistics Master’s programme at the time of application (usually in January) in addition to the credits needed for regular admission.

The following documents should be submitted with the application:

• Secondary school leaving certificate with an overview of subjects and
  grades, please refer to the country information in the application portal
• Overview of subjects and grades for your degree programme (Transcript
  of Records / Diploma Supplement)
• Module handbook (description of the learning content of your degree
  programme to date)
• Degree certificate from the university or, in the graduation phase,
  confirmation of when you will graduate
• Official translation of documents not issued in German or English
• Proof of the language skills required by the Subject-specific access
  and admission rules for the Master’s programme (see
  https://www.stat.de/wp-content/uploads/2.2.3.23.-2019-Statistik-E-3.pdf).
• self-assignment form on admission requirements and selection criteria.
  This form(s) is available as a PDF document on the application portal.
• Complete curriculum vitae (from the beginning of school education to
  the date of application)
• Copy of passport or identity card; if you have more than one
  nationality, all supporting documents
• If you are currently studying at a German/Austrian college/university:
  Certificate of enrolment stating the subjects and semesters studied.
• If you have already studied at a German/Austrian university:
  Exmatriculation certificate/confirmation of leaving with details of the
  subjects studied and the subject-related semesters.
• For applications from China, Vietnam and India: Certificate of the
  Academic Examination Centre (APS)

For further details see
https://www.hu-berlin.de/de/studium/bewerbung/bewerbung-und-zulassung/informationen-fuer-internationale-studieninteressierte/bewerbungsfristen-und-dokumente-zur-bewerbung-fuer-masterstudiengaenge
(in German).

Applicants from the People’s Republic of China, Vietnam and India need an APS certificate.

Yes. If you are missing ECTS, whether in Specialized knowledge 1 or in Selection criterion 2, you can use the time until the next application period to acquire the missing ECTS.

Acquire the missing ECTS in the winter term. Enroll in a bachelor’s programme for this purpose, e.g. in a bachelor in mathematics. Or enroll as a guest auditor or a visiting student and take courses. Please note that only courses that have been completed with an examination at a recognized higher educational institution can be recognized.

In the summer semester, you can already take basic courses from the master’s programme in statistics and have them recognized later if you have been accepted into the master’s programme in statistics.

Yes. All untranslated documents will not be considered.

No. Your application will be evaluated only by the documents you provided till the application deadline.

You have to apply at the HU Berlin as described on this website under Admission.

The semesters after receiving the Bachelor’s degree count as waiting semesters.

No. But you could register as guest student (“Nebenhörer”) to already take some courses in the summer semester and then apply for the winter term, for HU see the corresponding information of the course guidance centre on the HU website.