Will the decision tree just assign a known class to a new test example
with an unseen class?
Yes. A single decision tree assigns the majority class of the leaf to the given sample. So, if you have unseen classes in the test data, these (and possibly many) algorithms can't handle it.
I see you have any questions. Q&A sites like this are usually not best suited for such cases, I'd encourage you to ask one question at a thread next time. Also given the number of questions, it'd be probably a good idea to start with one of many great handbooks on machine learning. Nonetheless, I feel like the questions are fairly easy to answer, so let ...