Concept:
Pair production and annihilation involve conversion between matter and energy.
Step 1:
Electron and positron each have rest mass energy:
\[
0.51~MeV
\]
Total:
\[
1.02~MeV
\]
Thus A is correct.
Step 2:
Pair annihilation can occur without nucleus.
Thus B is correct.
Step 3:
For pair production threshold wavelength:
\[
\lambda \approx 1.2~pm
\]
Thus C is correct.
Pair production cannot occur in empty space and requires nucleus.
Thus D and E are incorrect.
Step 4:
Correct statements are:
\[
A,\quad B,\quad C
\]
\[
\boxed{\text{Correct Option = (1)}}
\]