Step 1: Check each statement against the rate laws:
Zero order: rate $= k[A]^0 = k$. First order: rate $= k[A]$.
Step 2: Statement (A):
Rate of a zero-order reaction is constant, equal to $k$, so it does not depend on concentration. False.
Step 3: Statement (B):
Thermal decomposition of acetaldehyde, $\text{CH}_3\text{CHO} \to \text{CH}_4 + \text{CO}$, has an order of 3/2. False.
Step 4: Statements (C) and (D):
For first order, setting $[A] = [A]_0/2$ in $\ln([A]_0/[A]) = kt$ gives $t_{1/2} = \ln 2/k$, no concentration term, so (C) is true. For zero order, $[A]_0 - [A] = kt$ gives $t_{1/2} = [A]_0/2k$, which depends on $[A]_0$, so (D) is false.
Final Answer:
Only statement (C) is correct.
\[ \boxed{\text{(C)}} \]