Is my transit at FRA to Amsterdam domestic or international?

You are correct that Norway is not in the EU -- but what matters for passport control is not EU membership, but Schengen, and Norway is in the Schengen area. So both your flights will be Schengen-internal.

In Frankfurt, when you get off your plane just follow the "connecting flights" signs until you reach an area where you see monitors showing lists of departing flights. Then locate your outgoing flight on the monitors and follow the signage towards the gate displayed for it.

Following the correct signs should not lead you through an exit immigration check.

Frankfurt airport is not separated into a ‘domestic’ and an ‘international’ area. Rather, the flights are allocated a gate and the gate number includes a letter for the area (A, B or C in terminal 1, D or E in termainal 2). Memorise the area that your gate is in and proceed there.

Once you have reached the area, signs will show you different directions for the gate numbers.

You should not encounter any immigration control on your way as all three airports in question (Oslo, Amsterdam and Frankfurt) are part of the Schengen area (as other answers have mentioned).

No, you will not go thru passport control in Frankfurt. It's actually a domestic flight.