Is there a passport control at Hamburg Airport or at German airports?

As others have already noted, while there are no systematic border checks within the Schengen area, you are expected to travel with valid proof of identity and might need to show it to the airline or local authorities.

That said, not only passports are acceptable for this purpose: National IDs work just as well. (Anecdotally, I've never carried my passport for intra-Schengen travel in the past decade.)

There is an official list of acceptable passports and ID cards by country. Norway seems to be issuing an ID card, so if you happen to have that with you, you should be fine.

Note that driver's licenses, which are often used as de-facto identity cards within many EU countries and also included on the list referenced above, are not considered valid identity documents within the Schengen area (even if they're in the ID-1 format and often "look and feel" just as official as identity cards).

Flying without a passport or an official government-issued ID (the EEA ID card) is a bad idea, because airline employees may want to see it at any time, most likely at boarding. Without one, you'll be denied boarding and of course lose money for your ticket. If you don't want to wait until you get an emergency travel document in Germany, you can do the following:

• Travel overland to Denmark. To be extra safe, I'd recommend crossing the border into Denmark using a local road (on foot, hitchhiking, by a local bus...). The announced temporary border checks are most likely limited to major roads and long-distance trains (I'd be very surprised if the entire Denmark-Germany border was heavily monitored).
• Once you're in Denmark, as a Nordic citizen, if you have any other picture ID (such as a driving license issued in the Nordic countries), your situation is much better. You can also fly from Denmark to Norway using only your driving license as an ID (source: https://en.wikipedia.org/wiki/Nordic_Passport_Union).
• If you don't have any suitable ID, you can try your luck and continue to Sweden by a ferry from Helsingør to Helsingborg (again, this is mostly used by local traffic and chances of a border check there are lower compared to taking a train from Copenhagen to Malmö). From Helsingborg, you can continue overland (train, bus, hitchhiking) to the Norwegian border.
• Once you get to the Sweden-Norway border, you should be fine. The border is only guarded by Norwegian border guards (not Swedish). As a citizen of Norway, you should be admitted to Norway even without an ID, but you may have to endure lengthy questioning and background checks (in the worst case). Alternately, you can also request an emergency travel document in Denmark or Sweden.

I personally had my passport stolen in another Schengen country (Italy), and I need to fly back to another Schengen country (coincidently Germany). I was also unable to get an emergency passport because my home (non-EU country's) embassy did not open before I was scheduled to fly out. I contemplated trying to just board my flight, but ultimately told the airline employees at the check-in counter about my situation and was given a special boarding pass. I did have a printed copy of my passport with me, which made this easier.

Based on my experience, I would recommend arriving early and talking to the airline at the airport, since it's in their best interest to get you home. I would've had to show an ID to board the plane anyways, so without the special boarding pass, I probably couldn't have gotten on.

I have also flown out of Berlin and Munich airport, and never needed to show my passport to board. But I would still recommend talking to the airline at Frankfurt, because their policies could be different there.

Your biggest risk here is that the airline will want to see your passport and deny boarding if you don't have one.

First of all you need to verify identity both for the airline at check in and for security. While the airline does not HAVE to check whether you have a valid passport, they sure CAN and they often do.

I found this to be very inconsistent: on some Schengen flights no one wanted to see any documents and on others they did check passports at check-in AND again at the gate when boarding. I don't think you can predict what exactly will happen.

Norway and Germany are both in the Schengen Area, so there should be no systematic checks for immigration purposes. However:

• There can be random spot checks
• Both have announced the temporary reintroduction of border controls
• Airlines may ask for ID for security purposes, especially if you have checked bags (though policies for this, including what documents are accepted, vary between different countries and airlines)

It is probably safer to report your loss and apply for an emergency passport. I’m surprised an emergency passport could take 3 weeks, that would probable be for a regular one. They could possibly also provide some other form of temporary ID allowing you to return to Norway.