Step 1: Define homolytic fission cleanly.
In homolysis a covalent bond breaks symmetrically. The two shared electrons split one-to-each, so each atom walks away with a single electron.
Step 2: Write the result of that split.
$\text{A}-\text{B} \xrightarrow{h\nu} \text{A}^{\bullet} + \text{B}^{\bullet}$. Both products are neutral free radicals, each carrying one unpaired electron.
Step 3: Test option (1).
It says one electron of the shared pair goes to one atom and the other electron to the other atom. That is exactly the symmetrical one-each split, so this statement is correct.
Step 4: Test option (2).
Electron-deficient and electron-rich species means cations and anions. Charged ions are the hallmark of heterolytic fission, not homolysis, so this is wrong.
Step 5: Test option (3).
An electronegative atom pulling both electrons again gives ions, which is heterolytic cleavage. Wrong for homolysis.
Step 6: Test option (4).
A simple carbon free radical is planar with the lone electron in a p-orbital, so it is $\text{sp}^2$ hybridised, not $\text{sp}^3$. Wrong.
Step 7: Conclude.
Only option (1) correctly describes homolytic fission.
\[ \boxed{\text{Option (1): each atom retains one electron of the shared pair}} \]