Step 1: Set up the situation.
Photorespiration starts when the enzyme RuBisCO grabs oxygen instead of carbon dioxide. We must judge each statement and keep only the correct ones.
Step 2: Check statement (a).
It says photorespiration does not occur in C$_3$ plants. In reality photorespiration is a typical feature of C$_3$ plants, while C$_4$ plants avoid it. So (a) is incorrect.
Step 3: Check statement (b).
It claims CO$_2$ is consumed and O$_2$ is generated. The truth is the opposite - O$_2$ is consumed and CO$_2$ is released. So (b) is incorrect.
Step 4: Check statement (c).
When RuBisCO works as an oxygenase, RuBP plus O$_2$ gives 3-PGA and 2-phosphoglycolate. So phosphoglycolate is formed and (c) is correct.
Step 5: Check statement (d).
Photorespiration is a wasteful path - no ATP and no NADPH are made, and fixed carbon is even lost as CO$_2$. So (d) is correct.
Step 6: Combine and conclude.
Only (c) and (d) are correct, which matches option 3.
\[ \boxed{(c)\ \text{and}\ (d)\ \text{only}} \]