I only have the magnetic credit cards not the chip/pin card. Can I still use my magnetic card in Sweden? What should I do if I cannot use my card?
I was in Sweden in 2014 with an American credit card, and it was accepted literally every place I used it, both ATMs and shops. (Two different cards.) I don't recall trying an automated ticket dispenser (e.g., bus ticket) which I think would be the most likely to fail.
Lacking a chip is not an issue. Almost all card readers are outfitted with both chip and magnetic strip readers. The only time I've seen a card reader without a magnetic stripe reader was in a food truck.
Not having a PIN is never an issue when there's a sales clerk around. You'll likely have to tell them that you don't have a PIN number (in Sweden, magnetic strip cards have PIN numbers too), but they should be able handle the transaction via a signed receipt instead.
Some vending machines do require PIN numbers (the vending machines used to top up the metro cards, most notably), but you can just visit a nearby Pressbyrån (a chain of convenience stores often located in the metro) or similar store to top those up instead.