They're supposed to charge 1kr per transaction, flat fee, but they've been putting it off. They're probably getting people used to the service before starting to charge for it. Taking a note out of the drug dealer's book I suppose.

Not as of now. But as Fnord mentioned, they might be charging 1 kr in the future which is fine.

If I were to guess how it works it would be like:

The receiver of a swish actually gets the money from their own bank while the sender actually just sends money this their own bank as well.

Then the senders bank will set a IOU to the receivers bank to balance things out and that will get fixed in a couple of days (the whole bank day transfers)

When the Swish service launched (2012) it was only consumer-to-consumer and no fees. Last year they added businesses and charge similarly to credit cards, fee on the creditor side.

For person to person / peer to peer - it's currently free. For person to business/organization it will cost the business 2.5 SEK per transaction as well as a monthly fee and/or an activation fee.

Prices may vary depending on at which bank the business/organisation opens an account and activates Swish to.