For warehouses, particulary for cubes, you need to start with 'what questions do I want to ask of the data?' This will help inform you of what are facts and what are dimensions. Incredibly short form: Facts can answer questions, Dimensions will describe facts.

In this case, it looks like you want to ask questions about the projects, so think of that as your fact table, and decide what questions you want to be able to ask of it, and then hang your dimensions off the resulting fact table.

This of course is not the only approach to warehouse building, but it's an excellent starting point if you're new to the process. Then take what you've learned and re-read all that material that's got you twisted around and it should make a TON more sense.

I know it's not what you're asking for, you're looking for a solution. I'm loathe to give you *my* solution because I doubt the questions I'd expect to ask of data are the ones that are actually on your mind.