I checked several websites, both Catholic and Protestant, and the consensus was what you are saying here. The only way to break a betrothal would have been for Joseph to issue a bill of divorce, following standard Jewish law. So, having a case of cold feet would not have been good enough, but fornication/adultery would have been a sufficient reason. This explains the language in verse 19, i.e. they had not had the marriage ceremony yet.
Yes.