There is a rule (a law?) - Ukrainians can’t be in EU for more than 90 days. Poland extended it to 180 days.
Is he getting his information from the Russian Facebook trolls?
As a tourist or on business you can come into Germany for 90 days without needing to register.
If you intend to stay longer then you need to register - just like the Germans. The reason is that cities, towns, and villages get their slice of funding by the government depending on how many people live there. So when you move to live somewhere else then you deregister at the place you were, and register at the place you now live.
Germany has a LOT of experience with taking in refugees - in the 90s they took in over a million from the former Yugoslavia (mostly Bosnia, but also Croatia and Serbia), in 2015-2018 they took in over 600,000 Syrians, and currently over 700,000 refugees and counting from Ukraine.
see https://www.macrotrends.net/countries/DEU/germany/refugee-statistics
There is an important distinction between “economic migrants” and refugees though - which is the reason why unlike other “refugees” that need to go through a lengthy process of being accepted as a refugee those fleeing war (like in Yugoslavia, Syria, Ukraine) get special treatment (eg the presumption that they really are refugees) and not only get a residence permit for 3 years on registration (which is expected to be extended if necessary) which means they are allowed to work immediately, but have their driver’s licence recognised too.
And absolutely NOBODY is being send back to a war zone after 90 days - that would be against the EU Human Rights Convention anyway.
The recommendation is to go to “Erstaufnahme-Zentren” (Centers for taking you in) that provide a place to stay (often decommissioned US Army barracks are being used for that), food, clothing, financial support, medical support, and importantly help with all the paperwork to get registered, get a Sim card, get health insurance (often provided for free by the health insurance companies), provide German language courses, and help you find a job and a place in the community (a lot of Germans have offered to take people in) or your own flat (the policy in Germany is to prevent ghettos so preferably you are housed within the general population) when you are ready to live on your own.
Two friends of mine in Germany took in Ukrainian refugees - in hindsight it would have been better to go the official route and use the “Erstaufnahme-Zentren” as the paperwork, getting health insurance, etc is way above what the refugees can deal with, and is even challenging for their German hosts.
He might also want to read this article from the Guardian.
Can someone tell Kyryl Pekarov that please?