Should I buy a Eurail Pass?

Only if you plan on traveling between cities every 2-3 days. If you are staying in base cities for 5+ days, point-to-point tickets bought 8 weeks in advance are significantly cheaper.

How do I deal with laundry?

Find a local 'wash and fold' or laundromat in each city. Never pack 21 days of clothes; pack for 7 and do laundry once a week.

How to plan a 3-week multi-city Europe trip

Limit your trip to three or four base cities to avoid spending your entire vacation on trains and planes. Use a hub-and-spoke model to anchor your stay in major cities and take day trips to surrounding areas.

Select your route. Pick one geographic region (e.g., Central Europe, Iberia, or the Mediterranean). Do not attempt to visit more than 4 major cities in 21 days or you will suffer from travel burnout.
Book an 'Open-Jaw' flight. Book your inbound flight into your first city and your outbound flight from your last city. This saves you from having to backtrack halfway across the continent to fly home.
Map your transport. Use the Eurail Planner or Omio to compare train versus budget airline costs. For distances under 4 hours, always choose the train; it drops you in the city center and avoids airport security.
Reserve accommodation. Book 5-6 nights per base city. This allows you to unpack, find a local coffee shop, and actually get to know a neighborhood rather than living out of a suitcase.

Should I buy a Eurail Pass?: Only if you plan on traveling between cities every 2-3 days. If you are staying in base cities for 5+ days, point-to-point tickets bought 8 weeks in advance are significantly cheaper.
How do I deal with laundry?: Find a local 'wash and fold' or laundromat in each city. Never pack 21 days of clothes; pack for 7 and do laundry once a week.