It seems that you will be using Ryanair for the intra Europe portion of your trip and that you will be getting to Europe on another carrier.
I hope that you realize that because your trip will involve two completely independent itineraries (USA-Europe, Intra Europe) if anything happens on either leg of the trip that affect the other one, ie.: late arrival of an aircraft, cancellation etc. then you will not have the benefit of being re-booked on another flight.

This is especially true for the return portion of the trip. If, for whatever reason, the FR flight out of Gothia does not arrive in time for you to catch your flight back to US then you will be in a real pickle.

There are enough case stories like that on www.ryanaircampaign.org as well as on www.airlinequality.com.

I would suggest that you:
1. double and triple check the spelling of each one of the 29 persons who are travelling on the confirmation you got from FR and make sure that they match letter for letter how their names are written in their passports. Even a single letter difference will mean that that person will not fly on Ryanair even if the mistake is due to their typo.
2. consider buying travel insurance, especially trip interruption insurance, that will help you in case you can not make either connection.

I would estimate that you have about 90% chance of successfully completing your trip, ie.: getting to Sweden and returning to US on the planned dates and the question is whether you are willing to take the 10% chance that you may get stranded in the connecting city.