Hello @Viki_Kysli,
welcome here, thanks for using Wefugees - and for a very important question!
In general, your driving licence is valid for six months here. But, as the Department of Motor Vehicles points out, you're principally not allowed to drive without insurance. Nevertheless, there will be some need to drive your vehicle, e.g., when you have to move. For that reason an initiative of German insurance companies has been started, that will cover potential damages until 31 of May.
You have to apply for a driving licence issued from German authorities before the six-month period expires. Please ask someone at your place for the address where to do so.
What is much more important:is the following: Without a liability insurance (Internationale Karte für den Kraftverkehr - International insurance card for motor transport) you shouldn't even dream of starting your car (after having entered German territory). The insurance is known here under the name "Green Insurance Card". You can get it here, under the condition that you had a liability insurance in Ukraine:
http://www.gruene-karte.de/de/ukrainische-fahrzeuge-in-deutschland/
Please read the information carefully, which is also available in Ukrainian.
Hopefully, I could clarify your question.
I hope my answers were helpful and I’ll be very pleased if you contact me again with further questions. I'm a member of the mbeon-staff and I‘ll be glad to guide over a longer period of time. mbeon is an online advisory service for migrants via the mbeon-app, which you can download on your smartphone for free. You'll find me in the mbeon-app under my location „München” and then my name “Frau Müller“ and get confidential one-to-one advice in a safe virtual room where nobody can read messages. For further information please visit www.mbeon.de.
Best regards
mbeon-Christine