Do I qualify for a German visa? How do I apply? [closed]

This is probably not what you want to hear, but there is absolutely no chance that you will get the necessary paperwork done by June 15th.

You seem in general very little prepared and some of your alleged problems do not match publicly available information from the German Embassy in London. VisaMetric is completely irrelevant for your case. For your studies, you need a long-term national visa (type D) and/or a residence permit and applications therefore are handled directly by the embassy. VisaMetric is only handling applicatins for short-term visitor visas (type C).

Even if the embassy is closed for most purposes, they are still accepting and handling applications for long-term visas under certain conditions:

Visa applications are currently not being accepted by the German Embassy in London and the Consulate General in Edinburgh Due to the entry restrictions on all non-essential travel from third countries to the Federal Republic of Germany to contain COVID-19, the German Embassy in London and the Consulate General in Edinburgh are currently not accepting any new visa applications. An exception may be made if the applicant can demonstrate the existence of compelling reasons that justify entry under the current rules.

AFAIK, this has been the case during the entire lockdown. Even though all unpostponable services have been suspended during the lockdown, there has been no complete closure of the embassy.

The German Embassy in London does not publish any processing times for long-term visas, but even without any corona restrictions, you should have planned at least several months. Had you applied for a visa mid March, before the lockdown, it would still not have been obvious that the application had been processed before June 15th.