Did I calculate this MOSFET circuit correctly?
$$\text {You already obtained the correct value for }R_2.$$
$$\text {I don't know how you calculated } R_D, \text {but it should be calculated as follows:} $$ $$ \text {At } U_B = 12V,$$ $$ R_D = (U_B - U_{DS})/50ma = (12V - 6V)/50ma = 120 ohms.$$
$$U_{Dmax} \text { is obtained when }U_{DS} = 0,  (12V - 0) = 12V.$$ 
$$I_Dmax = U_{Dmax}/R_D = 12V/120 = 100ma$$
$$\text {At }U_{DS} \text{= 6V, } U_{GS} \text{= 6V, } \text {and }I_D=50ma, \text {it is operating in the "saturation" region.}$$.
$$\text {The saturation region ($U_{GS}$ = 6V), is any point to the right (higher voltage) of $U_{DS}$=5V.}$$  

$$\text {To shift the operating point into the linear region, you have to decrease the drain }$$

$$\text {current to around 32ma, which gives }U_{DS} = 2V.$$
$$\text{I calculated the gain }\beta\ \text {to be about 8ma/V.$$ Using this, and the given formula,}$$ $$\text {one obtains: $I_D$ = 8 [7-1 -(2/2)] x 2 = 80ma.}$$

I hope that by understanding how I obtained the various answers, your errors and confusion will be gone.