What’s the relationship between German and Polish languages?
What do they have in common and how are they different from each other?
German has 4 cases, but Polish has 7 cases. Both have 3 noun genders.
I don't know specifically about Polish, but I am learning Russian, and have studied German and Spanish.
As you know, they are both Indo-European languages and thus have some developments in common. I see this in Russian, with the dative case being very similar to Ger/English, plus many words sharing a similar form or apparent descent.
The other thing is that the Germanic and the Slavic peoples were the same people (more or less) and have been neighbours since the Indo-European speaking people arrived there after the Flood of Noah, (arrival in Europe c 2000 BC) until the populations grew and the tribes moved apart, developing their languages independently thereafter. This might have been around 1000 BC or a little later.
So they share a history and development of the IE language for more time and developments that the other branches of the IE group. They have been neighbours ever since, together with the Baltic peoples, and there has been some cross migration which would have brought new words from Germanic to Slavic people, and Slavic words to Germanic peoples, just like it did in with the Germanic, Huns, Alans, etc when they migrated into Roman territory. Large numbers of Goths migrated into Ukraine and eastern Europe; Vikings traded along the rivers and into Byzantium for hundreds of years; Sweden had empire ambitions on the Baltic coasts, but more importantly, in the area of Prussia there has been mixing of population and languages for the past thousand years.
All IE languages had originally 3 genders I think. Language is devolving, not evolving. The number of cases has decreased in most of the languages, which makes it easier for iTalki students to get their heads around learning odd grammar.
In Silesia there are some German words, as it was once part of Prussia. Dankuje (I do not know the spelling) means thanks you and is related to the German word 'danke'. Cirkaabau (again no idea how to spell it) is a combination of 'circa' and 'about'. (There are about/around 3000 people). Blitzkrieg gibt es auch.
Hier noch eine lange Liste: https://de.wikipedia.org/wiki/Liste_deutscher_W%C3%B6rter_in_anderen_Sprachen
Both languages have a common Indo-European "ancestor", but they have been separated for long enough to develop quite different features. Usually, it requires quite a bit of linguistic knowledge to identify cognate words. For example "zwei" and "dwa" still might be recognizable as cognates, but what about "fünf" and "pięć", which are related as well? Then the languages have also exchanged some loanwords more recently. These are easier to spot.
Grammar-wise, Polish has retained 7 of the 8 Indo-European cases, while German has kept only 4 of them. The cases which are used in both languages have a similar usage. But then, you have the 3 additional Polish cases which are mostly expressed using prepositions in German. The verb conjugations are quite different between the two languages. The tense systems work differently, and then you have the concept of verbal aspect in Slavic languages which doesn't exist in German. As a Chinese speaker you might have an advantage here, because particles like 了 and 过 express quite similar concepts to the Slavic verbal aspects. At least, my Polish helped me to learn this bit of Chinese.
In short, when you learn Polish on top of German, you will find only very few similar words and grammatical forms. But you will still find some faint similarities between the languages, when you look at them from a greater distance as a non-Indo-European speaker.