You can forget a first hand contract from the municipal housing agencies. Second hand contracts and/or private landlords still work - but watch out for scams.
last I have read it's 10 years in Stockholm, in Åkersberga (less than an hour north of Stockholm) it would be a few years https://www.armadafast.se/boende/bostadsk%C3%B6/k%C3%B6tider
or you can buy for 2M SEK (200,000 Euro) a nice small house in a suburb and pay the mortgage back over 50 years.
Where I was living — in Majorna/Kungsladugård — on average 2,400 people applied to rent each apartment. This was back in 2012. This would be worse now, given the refugee/migrant influx.
Barely. There is a black market for rental contracts in Sweden, which is as far as I'm aware unheard of everywhere else in the world.
Renting "i andra hand" (subletting) is extremely difficult. Want to see how bad the market is? Put a fake apartment up for rent on Blocket to test the response rate. The last time I did this, I had over 300 responses in the first half hour.
Subletting is also time-limited to a year, if I remember correctly (though perhaps some housing associations have different rules on this, and perhaps not).
The people downvoting my original comment which is somewhat critical of Sweden is good reflection of the typical Swedish mentality — borta bra men hemma bäst. There's a reason Sweden is called "China of the North".