I am an MMath graduate of Warwick this year.
The MSc is almost completely 'identical' to the 4th year of the MMath course (except some differences in monitoring points/supervision). You need to take at least 120 CATS and at most 150 CATS of 3rd or 4th year modules. Each module is 15 CATS and out of those 120-150 CATS must contain at least 105 CATS of 4th year modules (or so called List C modules). The dissertation is 30 CATS (a 30-40 page research paper typed up in Latex) so you need to do at least 5 more 4th year modules. Everything is optional except the dissertation so you can take modules freely from each term although you should aim for a balance between Terms 1 and 2. The course is called MSc to distinguish people who came to Warwick from other universities for their 4th year. You cannot apply JUST for the 4th year of the MMath course.
Not very sure about the Diploma + MSc but your guess should be right since there are a lot of 4th year modules offered every year. The project and dissertation are actually the same thing since for 4th years we call the dissertation our 'project', so I suppose you would have to offer 2 pieces of work, one in each year.