Step 1: Check statement (I).
Calgon is sodium hexametaphosphate whose formula is
\[
Na_6(PO_3)_6
\]
Hence, statement (I) is correct.
Step 2: Check statement (II).
Exhausted permutit used in water softening is regenerated using concentrated sodium chloride solution:
\[
NaCl
\]
It is not regenerated using
\[
KCl
\]
Hence, statement (II) is incorrect.
Step 3: Check statement (III).
Calcium stearate is a soap-like compound and is insoluble in water.
Therefore, statement (III) is incorrect.
Step 4: Check statement (IV).
In the crystal structure of ice, each oxygen atom forms hydrogen bonds with four neighboring oxygen atoms in a tetrahedral arrangement.
Hence, statement (IV) is correct.
Step 5: Identify the correct statements.
The correct statements are:
\[
(I)\ \text{and}\ (IV)
\]
Step 6: Final conclusion.
Therefore, the correct answer is
\[
\boxed{\text{I \& IV only}}
\]