I finaly got my XR-2206 (Monolithicv Function Generator IC) chips.

The voltage level of the different waveforms differs significantly.

Sine 4,8 → 6,8V
Triangle 3,3 → 8,3V
Square 0-12V

My questions are:

How do I change the offset of the sine to 0-2V and triangle to 0-5V.

If it is possible to change the offset would a simple voltage divider be a “good way” to adjust the triangles voltage to 0-2V?

I am thinking about using a CD4016 and a CD4051 demultiplexor to digitally control the different waveforms (see picture), but it will not work if the offset differs between the waveforms.

One way is to run them thru a capacitor to get a 0 +/- signal, then use 2 resistors from +5 to GND to bring the center point to where you want it. And resistor divider to bring the levels down.
Can do similar with op-amps so there is drive capacity to get the signals thru the analog switch.

I tried to run the signal through a capacitor and got a fine -1 to +1 sinewave.
But I don't understand what to do with the resistors. If I put one resistor to 12V and one to GND the signal goes to 5,7 -> 6,2V.
The centerpoint changes but also the amplitude (0,5V instead of 2V).
Shouldn't the signal be 5-7V? (The resistors was 2*10K).

What value of capacitor did you use. The reactive impedance of the capacitor will form a voltage divider with your offset resistors. To minimise the divider loss you should be looking at a value that has an XC of no more than 1/10th the value of your offset resistors at the lowest frequency you are working at. Ideally it should be even less but you then have to balance performance with practicality.
For example, let us say the minimum frequency you are interested in is 100Hz.
XC = 1/(2 x pi x f x C) hence C = 1/(2 x pi x f x XC) where f = minimum frequency and XC = 1kohms
At 100Hz we therefore get a value of C = 1.5 microFarads.
If this value produces satisfactory results at 100Hz, it will perform OK at higher frequencies.
If you want to consider lower frequencies you will need to increase the capacitor to meet the criteria.

For the voltage shifting, try using higher value resistors, like 200K to 12V, the cap, and then 100K to Gnd. Output should sit at 4V and wiggle up/down from there (3V to 5V).