Can American mattresses fit in a German bed frame?

Maybe. European mattress sizes are different from US sizes, in a way that's not trivial to explain. In terms of length, most European mattresses are longer than the US standard sizes (while being slightly shorter than US "XL" sizes), but the width can be either more or less depending on the specific mattress size you're talking about

Many bed frames are designed in such a way that it's possible to use a somewhat smaller mattress as long as you don't mind a bit of extra space around the edges. Also, a lot of frames make an allowance for thick bedclothes, and you may be able to get away with a (slightly) larger mattress than it was technically intended for. However, it's probably not going to be possible to use a US "King" mattress in a German "King" frame, since the US version is about 5 inches wider than its German counterpart.

You'll need to get the actual dimensions for the frame/mattress and compare.