Or do I need to buy separate tickets?
In Germany, the Eurail passes are usable on regional trains, as well as the S-Bahn, in cities, nothing else. So, don't plan on using your pass much on days where you travel only in a city.
Depends on where you are going. The pass is good on almost any local or regional train in every country. However, as posted on the Eurail website, there are reservation and supplemental fees for premium trains in every country as well as the night trains. In Switzerland, you will find that the Eurail pass will only get you a 25% discount on any transporation from Interlaken into the Lauterbrunnen Valley and up to any of the alpine villages. In Italy, you will pay an extra 15E-20E on top of your Eurail pass to ride any of the Eurostar-class trains.