While you might be able to physically set foot in all those places within your week's time frame, you would't actually be able to see anything since you'll always be on the go. You could easily spend a week in a city like London, or Paris, and barely scratch the surface. My suggestion would be to pick 2, max 3 of the places on your list and actually spend a bit of time in each place.

As for your original question:

- One-way car rentals in Europe: In my experience, returning to a different city in the same country is generally permitted and costs little to no extra. Returning to a different country, however, is cost prohibitive. Car is particularly useful if you want to go to some out of the way places that don't have rail service. For 3 people, it can be a reasonable value, even considering tolls and the high price of petrol.

- Train network in western Europe is very well developed. If you want to go from city to city, this is the way to go. Cost is moderate, but trains are particularly convenient in that they deliver you into the city center, and you can see some scenery long the way. If you want to travel longer distances, look into the overnight trains to maximize your sightseeing time. Also, check into a regional Eurail pass, depending on your plans it might suit your needs for cheaper.

- LCC (particularly Ryanair) can sometimes be cheaper than trains if you're flexible with your travel plans, book far enough in advance, and follow their rules to the letter. But you'll find their schedules and routes much less convenient.