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Archaea and bacteria are prokaryotic organisms that have very simple cells. These organisms do not have any cell organelles. Even the nucleus lacks such cells; hence, the genetic material, either DNA or RNA, is stored within a nucleoid structure.

The prokaryotic Archaea produce membrane lipids called isoprenoid lipids. The prokaryotic bacteria produce membrane lipids called fatty acids. The differences in the lipid component of these prokaryotes are due to the composition and characteristic features of the cell wall.

Hence, Archaea and bacteria produce different membrane lipids.

Therefore, the given statement is true

The cell wall of Archaea comprises substances called polysaccharides. These polysaccharides are proxy substances that are present instead of peptidoglycan. It helps in providing structure and rigidity to the cell and prevents any damages from occurring.

Hence, Archaea and bacteria do not have peptidoglycan.

Therefore, the given statement is true.

Most prokaryotes that are alive do possess histones. Due to the absence of histones, the DNA is tightly coiled through supercoiling. However, the only organisms in the prokaryotic kingdom that have histones associated with DNA are Archaea.

Hence, only Archaea have histones associated with DNA and not bacteria.

Therefore, the given statement is not true.

Archaea are sub-classified into different categories. One such category is called methanogenic archaea, which are the only organisms capable of using carbon dioxide to oxidize hydrogen. During this process, methane gas is liberated as a byproduct.

Hence, methanogenic Archaea are the only Archaea that use carbon dioxide.

Therefore, the given statement is true.