Faroe Islands:
Scandinavian and EU citizens (Austria, Belgium, Bulgaria, Croatia, Republic of Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain and Sweden) do not require a VISA, however, at all times it is necessary to bring along a valid passport. The traveler is always responsible to have valid travel documents to show when necessary.
You can find more information here http://visitfaroeislands.com/plan-your-stay/before-you-arrive-in-the-faroe-islands/passport-and-visas/
Iceland:
Iceland joined the Schengen states on March 25, 2001, an agreement of 26 states to abolish checks at their common borders on the movement of persons and facilitate the transport and movement of goods at those borders.
The validity of the passport or recognized ID card must be at least three months beyond the proposed stay, except for citizens of EEA/EFTA countries. Those documents only need to be valid beyond the stay in Iceland.
For information on passport and visa requirements, please visit the website www.utl.is
do we need passports to travel from seydisfjordur to hirtshals and back with our national ids?
I do not know.