I am Turkish but I live in Sweden and I own a permanent residence there. Passport is Turkish and all but I have an ID (local ID just for Sweden) and the residence card. So do I have to check in at the airport with Ryanair again although I had already checked online earlier this week? Or just head straight to the gate? I am flying from France to Sweden.
According to Ryanair's own rules which you can find here, they do in fact require non nationals to present themselves at their counter to have their travel documents checked. That applies to you as their website doesn't distinguish between nationals and residents (confirmation through customer service pending)
6.4 All non-EU/EEA citizens must have their travel documents checked and stamped at the Ryanair Visa/Travel Document Check Desk before going through airport security.
Also note that since they won't stamp your passport, you'll need to print your boarding pass so make sure to factor in more time.
If you've already checked in online there's nothing else you need to do, unless you want to drop off bags in which case you'd need to head to their counter and wait in line. Otherwise you can just head straight to the gate, passing security on the way. There's no other immigration checks within the EU.
Most airlines, Ryanair included, accept an electronic or mobile boarding pass now, so you don't even need to print it.