I'm flying from Beirut to Stockholm via Frankfurt as a tourist. In Frankfurt I had to show my passport to immigration but when I got to Arlanda airport (Stockholm) I got my bags and left without passing through immigration. I just followed other passengers. Is that normal? Don't I have to check with customs? Not even check my bags?
Customs and immigration are seperate. Immigration is about you, customs is about your stuff.
For countries in the Schengen area, Immigration is handled at your point of entry to the area. In your case that would be Frankfurt. The procedures will depend on your citizenship. Once in the area there will not normally be further immigration checks.
Customs on the other hand is NOT centralised. You normally go through customs at your final airport after baggage claim. Customs in the EU usually uses a Lanes system.
- Blue lane: From inside EU with nothing to declare.
- Green lane: From outside EU with Nothing to declare.
- Red lane: Goods to declare.
Sometimes instead of the lanes there may be a red phone. Sometimes there may be no blue lane (in which case use the green one instead).
It is your responsibility to determine whether you have goods that need declaring. If in doubt you are supposed to take the Red lane (or use the red phone) and speak to a customs official. Entering without speaking to customs is legally considered to be a declaration that you have nothing to declare.
Random checks and intelligence driven checks are possible in the Green and Blue lanes.
Yes it's normal. Sweden and Germany are both part of Schengen as well as the European Customs Union, so once you've cleared immigration in Frankfurt the last flight is kind of like a domestic one so you won't pass immigration again.
Note that customs isn't the same as immigration, so unless you have something to declare your customs check, which should be done in Sweden, is just walking down the 'nothing to declare' lane.
Immigration formalities are done in Frankfurt (your point of entrance in the Schengen area). That's where you were admitted to the Schengen area, your passport stamped, etc. so it's perfectly normal not to undergo an immigration check in Stockholm. Even if the police in Sweden wants to see your passport (which might happen), this would not be an official "external" Schengen border check.
By contrast, customs formalities have to be completed in Stockholm. In continental Europe, you don't necessarily need to talk to anybody nor to fill a landing card or anything like that but walking down the green "nothing to declare" lane amounts to a declaration of sorts. It happens relatively rarely but it's also entirely possible for customs agents to stop you and/or ask to see the contents of your luggage at this point.
If you do have something to declare (perhaps you have a lot of cash with you or you are coming back from a trip with expensive goods), then you are supposed to go through the red lane, fill in the relevant forms and/or pay duties and taxes in Sweden.
For border purposes, Germany and Sweden are in the same country, the Schengen Area (that's why they have a common visa, the Schengen visa). So you'll enter at Frankfurt and then continue on a "domestic" flight to Sweden.
There will be a customs corridor, but you can just walk down the green lane and you'll usually be out in 30 seconds