We're taking the train from Paris to Munich in June. It stops in Stuttgart at 15:04. The train departs at 15:12 for Munich. Is 8 minutes adequate time? Does it show the platforms of arrival & departure? If not, do we book our reservation separately - Paris to Stuttgart; and Stuttgart to Munich?
That is common and should be enough time. Be at the door ready to get off with the train stops. You booked your reservation as one - Paris to Munich with a train change. Just like you do with the airlines.
If you book the entire route well in advance (up to 92 days allowed) on the German Rail site, you can get a discount fare.
According to the Bahn website, your train will come in on track 6 and the train to Munich will go out on track 15. Here is the layout of the Stuttgart Hbf. As you can see it is a "dead end" station, with trains coming in and leaving at the same end. There is a connecting platform at the track ends connecting all the individual platforms. There is also a tunnel in the middle that connects the platforms. The transfer is doable, but you can't waste time. As Frank says, before the train stops in the station, be at the door with your luggage, ready to get off. If you are near the front of the train, walk in the same direction as the train was going to the connecting platform and walk over to platform 15. If you pass the stairs on the way, go down to the tunnel and over to platform 15. If you have excessive luggage, there will probably be free luggage carts on the platform. In case you use one, the connecting platform will work better. There will probably be others making the same transfer. Stay with the herd. The conductor will be on the platform and is not going to release the train while people are getting on. If you are really worried about the time, there is another ICE leaving for Munich at 16:12. That will give you an hour and eight minutes for the change, time to get lunch in the station. No need to get two separate tickets. You can schedule the stopover when you book your tickets online from the Bahn. From the Bahn query page, enter Stuttgart where is says "stopover" (you might have to click "Change other data" to see it), then "1:00" for the time. This will get you a schedule with at least an hour (in this case 1h8min) in Stuttgart.
Continued If you book a discount (Europa Spezial) ticket, it is train specific. The ticket will only be valid for the specified train from Stuttgart to Munich. In case you are using a discounted fare, and the train from Paris is late causing you miss the Munich train, go to a ticket counter. The Bahn will put you on the next available train to Munich.