Step 1: Amine solutions and regeneration.
Amine solutions such as MEA (monoethanolamine) and DEA (diethanolamine) are widely used to remove acid gases like H$_2$S and CO$_2$ from natural gas streams. These solutions are \emph{regenerable} by heating in a regenerator/stripper column. Therefore, statement (A) is incorrect.
Step 2: Absorption of H$_2$S by amines.
Amine solutions in liquid form react chemically with H$_2$S and CO$_2$ to form soluble salts. This is the fundamental principle of gas sweetening. Hence, statement (B) is correct.
Step 3: Glycol behavior.
Glycols (such as MEG – monoethylene glycol and TEG – triethylene glycol) are hygroscopic and used for gas dehydration. In the presence of oxygen, they degrade and form organic acids which can cause severe corrosion. Thus, statement (C) is correct.
Step 4: Iron sponges.
Iron sponge (iron oxide impregnated on wood chips) is commonly used for H$_2$S removal through chemical reaction forming Fe$_2$S$_3$. Therefore, statement (D) is false.
Final Answer:
\[
\boxed{\text{Statements (B) and (C) are correct.}}
\]