What do we need to submit for a visa application for residency in Germany?
None. As EU citizens, you cannot get German visas. As noted in the other answer, you have to register when you move there, but the only document you need is a Croatian passport or ID card. This is explicit in the free movement directive, 2004/38/EC. Article 6(1):
As European Union citizens, you do not require a residence permit to live in another European Union country.
Some countries (like Poland) require you to apply for a residence certificate after taking up residence.
Germany does not, but you are required to register at the local registration office (Meldebehörde) in the same way as a German citizen must.
Poland taxes based on residency, not citizenship.
Therefore, being a Polish citizen should not make any difference on your general taxation status so long as you don't live in Poland.
However, tax is a complicated subject and is subject to double taxation agreements between countries. As such, then that agreements between Poland and UK might be different ...