Is it right to apply superposition theorem to the RC circuit with non-zero initial capacitor voltage?
Yes, you can use superposition -- once for the V source, and once for the cap decay.

The cap decay is (set the other V to 0) Vc=2+(0−2)(1−e(-t/RC)), or 2.e(-t/RC) [you missed a '-' in the exponential]

The 8 V source adds Vc += 8(1-e(-t/RC))

Two 4 V sources would each add Vc += 4(1-(e-t/RC)).

They all add together as expected.