Since MLlib uses Breeze under the hood is there a way of using MLlib with Breeze datastructures so that I do not need the whole Spark ecosystem but can still use MLlib only locally?
You can't do that. You can't use spark-mllib without spark-core even if the dependency can be pulled.
Nevertheless, if you want to run algorithms from MLLib in a standalone manner, you'll need to install spark in a standalone mode. No need for a real cluster in this case but the solution obviously won't scale.