You don't need 'sitting' to convey the sense in English. 'There is a fox on your bed' is also ok.
Maybe not, in general everyday conversation. But he verb used in the Czech sentence is "to sit," and the fox in question is clearly described as "sitting" on the bed, as opposed to lying or standing or jumping or playing...
"a fox is sitting on your bed?" Why it is not a variant ?
It is. Use the report button to report missing translations, but first double-check your answer.