Aufenthaltserlaubnis

Hi. I am in Germany since 2 month. I am from Moldova, so I don't need a visa for 90 days. I have applied to studies but takes time to have the letter. How can I be in Germany temporary. I have a German friend...he can be a guarantee for me to obtain a temporary residence here, if I have insurance and place to live? Who knows...I called Auslaenderbehoerde but they don't answer.

Call the office again when they are opened. Maybe you tried on Tuesday which was a holiday.

I have tried 3 days. Even today. The terminal online are in July available

You can send them email - some foreigner offices respond better to that.
But to answer your first question: Your current (Schengen tourist) visa allows only a stay of 3 months within a 6 months period. Thus to stay longer, you need another (possibly residence) visa - and a legitimate reason for getting one (a friend who offers to pay your upkeep and deportation cost is not enough).
If you cannot get another visa, you should leave the Schengen area for three months, or until you get your student visa.