Questions about the modified merkle patricia tree

I am trying to fully understand the modified merkle patricia tree used in ethereum. I have been reading the yellow paper and tried to consult google, but there are still some things I don’t understand.

1. In the yellow paper it says that for branch nodes “The 17th item is used in the case of this being a terminator node and thus a key being ended at this point in its traversal.” - If all keys have the same length, how would this ever be the case? Is this tree structure used anywhere where the keys are not guaranteed to have the same length?
2. I don’t understand how to structure an extension node. The formal definition seems circular to me, as c(J, i) depends on n(J, i) in the case of an extension node, but n(J, i) depends on c(J, i) for all cases where J is not empty. What am I missing here?
3. I don’t understand how the root hash is actually calculated, but I think this might be related to my question above. The way I understand (213) in the yellow paper, the root hash is calculated as the keccak256 hash of the RLP-serialisation of the structural composition of the root node. But how does the structural composition of the root node depend on the tree in such a way that any change below invalidates is?