Concept:
Coral polyps thrive in warm, shallow, clear and sediment-free tropical waters where sunlight can penetrate easily. Coral bleaching is a stress response caused by high temperatures and often leads to coral death if prolonged; it is not a survival mechanism.
Step 1: Evaluate each statement.
\[
\begin{aligned}
A.&\ \text{True. Reef-building corals are mainly found in tropical oceans and seas.}
B.&\ \text{True. Most reef-building corals occur in shallow waters, generally within about 200--250 feet.}
C.&\ \text{True. Clean, sediment-free water is essential for coral growth.}
D.&\ \text{False. Coral bleaching weakens corals and may eventually kill them.}
\end{aligned}
\]
Step 2: Identify the correct combination.
\[
\boxed{
A,\ B,\ \text{and}\ C
}
\]
Hence,
\[
\boxed{\text{(C)}}
\]