Can we take one slab of $p-$type semiconductor and physically join it to another $n-$type semiconductor to get $p-n$ junction?

If no external voltage is applied across a $P-N$ junction,there would be:

Out of the following,which one is a forward biased diode?

$A$ $2 \text{ V}$ battery is connected to a diode in forward bias. $A$ voltage of $0.5 \text{ V}$ is dropped across the diode,which is independent of the current flowing through it. $A$ current greater than $10 \text{ mA}$ causes excessive heating and damages the diode. If a current of $5 \text{ mA}$ is required in the diode,what value of series resistance must be connected in the circuit?

Current $I$ through a given $p-n$ junction when a voltage $V$ is applied across it is given by $I = I_0 \left( e^{\frac{V}{2 V_T}} - 1 \right)$, where $I_0$ and $V_T$ are constants. If $r_d(I)$ is the dynamic resistance of the junction, then $r_d(1000 I_0) = \alpha r_d(10 I_0)$, where $\alpha$ is approximately equal to

In a $PN-$junction diode: