Apr 11, 2016 - 2:04 PM
Welcome to MySwissAlps, laksmanmdu!
Here are some answers:
1. An 8 day Swiss Travel Pass starting on May 20 will be valid up to and including May 27 (or, to be more specific, up to 5 am on May 28). Which start date is best depends on your plans for May 20 and May 28. If you use one of these days for short local trips (exploring Basel for example) outside of the Swiss Travel Pass validity duration, you won't have many additional costs. If you book a hotel in Basel for your lastnight you'll get the free Mobily Ticket that allows free traveling to the airport on May 29. Please find details here. Please see our Swiss Travel pass page for all information regarding this pass, including purchase options (since you're from the Netherlands, www.treinreiswinkel.nl and www.swissrailways.com/ en are ecommended) and a validity overview.
2. If you're looking for just one base that allows you to cover all destinations as day trips, I'd recommend Interlaken or nearby town. This will still result in pretty long traveling distances, but in all it's the most central location. Jungfraujoch and Grindelwald are close, Lucerne/Titlis and Zermatt can be done as day trips if you don't mind leaving early and returning late. Please consult the timetable and the "Route" tabs on our attraction pages to get a feel of traveling times. If you feel they're too much, I'd recommend two base towns (e.g. Lucerne and Interlaken) instead. You can check the hotel pages for Interlaken and Lucerne I linked to. If you're not able to find good options there, please post to our accommodation forum.
3. No, personally I wouldn't recommend a car for the trips you have in mind. Quite some destinations are car free, strict traffic rules apply and driving in the mountain requires you to pay close attention to the road, rather than to the beautiful views. Please find more information in our train traveling and car traveling sections.