Design flaws when designing a MAC-function
Collision resistance is usually a property of hash-functions, would that also be a proper term to describe block-ciphers?

Well, kind of.
The message space of a hash function is huge. It contains about 2 ^ 2 ^ 129 separate messages for SHA-512, for instance. So it will have collisions as the output size is limited to 512 bits.
On the other hand a keyed block cipher is a permutation, a mapping from all input elements to a specific output element each. As all the input is mapped to a unique value in the output, there cannot be any collisions on the block cipher itself.
You haven't specified any method of using the block cipher for messages with a different size than that of the block size. If the block cipher is used in a specific way then you may well have a possible collision and therefore collision resistance when those are hard to find. Many hash functions are build on top of block ciphers after all, but it depends on the block cipher specifics and the way that it is used if that's secure.