Step 1: Understanding Archaebacteria.
Archaebacteria (Archaea) are primitive prokaryotes that survive in extreme environments such as high salinity, high temperature, and anaerobic conditions. Their cellular structure is fundamentally different from eubacteria.
Step 2: Analysis of statement (1).
Halophiles (salt-loving) and thermoacidophiles (heat and acid-loving organisms) are well-known groups of archaea. Therefore, statement (1) is correct.
Step 3: Analysis of statement (2).
Archaebacteria do NOT contain peptidoglycan in their cell wall. Instead, they may have pseudopeptidoglycan or other protein-based structures. Hence, statement (2) is incorrect.
Step 4: Analysis of statement (3).
The cell membrane of archaea contains branched chain lipids linked by ether bonds, which provide stability in extreme environments. Therefore, statement (3) is correct.
Step 5: Analysis of statement (4).
Methanogenic archaea produce methane from organic matter such as animal dung in anaerobic conditions. Hence, statement (4) is also correct.
Step 6: Final conclusion.
Since only statement (2) is incorrect, it is the correct answer.
\[
\boxed{(2)}
\]