Is it worth buying a rail pass?

Only if you are traveling across multiple countries in a short period. If you are staying in one region, point-to-point tickets booked 4 weeks early are almost always cheaper.

How do I avoid tipping?

You don't need to avoid it—it isn't expected. Service is included in the price. Rounding up to the nearest ten for good service is appreciated but never required.

How to Travel Scandinavia on a Budget

Save money in Scandinavia by skipping alcohol at bars, shopping exclusively at discount grocery stores like REMA 1000 or Netto, and utilizing free public infrastructure like city bikes and parks. Booking regional trains or buses at least 30 days in advance can cut your transport costs by up to 60%.

Master the grocery store. Eating out is prohibitively expensive, often costing $30+ for a casual lunch. Visit local discount chains (REMA 1000 in Norway/Denmark, Netto in Denmark, Willys in Sweden). Focus on 'private label' brands and shop the clearance bins for items expiring that day, which are often marked down by 50%.
Cut the alcohol costs. Alcohol is taxed heavily. A single beer in a bar can cost $12. If you want a drink, buy it at a 'Systembolaget' (Sweden), 'Vinmonopolet' (Norway), or a standard supermarket (Denmark) and drink it at your accommodation. Skip the nightlife scene if you are on a strict budget.
Utilize tap water. Never buy bottled water. Scandinavia has some of the world's cleanest tap water. Carry a reusable bottle and refill it everywhere; you will save about $4 per bottle.
Use regional transport passes. Don't buy single-ride tickets for public transit. Purchase 24-hour, 48-hour, or 72-hour city cards which include unlimited transport and free museum entry. Always check for student or senior discounts if applicable.

Is it worth buying a rail pass?: Only if you are traveling across multiple countries in a short period. If you are staying in one region, point-to-point tickets booked 4 weeks early are almost always cheaper.
How do I avoid tipping?: You don't need to avoid it—it isn't expected. Service is included in the price. Rounding up to the nearest ten for good service is appreciated but never required.