DNA, RNA and proteins are major biological macromolecules that coevolve and adapt to environments as components of one highly interconnected system. We explore here sequence/structure determinants of mechanisms of adaptation of these molecules, links between them, and results of their mutual evolution. We complemented statistical analysis of genomic and proteomic sequences with folding simulations of RNA molecules, unraveling causal relations between compositional and sequence biases reflecting molecular adaptation on DNA, RNA and protein levels. We found many compositional peculiarities related to environmental adaptation and the life style. Specifically, thermal adaptation of protein-coding sequences in Archaea is characterized by a stronger codon bias than in Bacteria. Guanine and cytosine load in the third codon position is important for supporting the aerobic life style, and it is highly pronounced in Bacteria. The third codon position also provides a tradeoff between arginine and lysine, which are favorable for thermal adaptation and aerobicity, respectively. Dinucleotide composition provides stability of nucleic acids via strong base-stacking in ApG dinucleotides. In relation to coevolution of nucleic acids and proteins, thermostability-related demands on the amino acid composition affect the nucleotide content in the second codon position in Archaea.