Short answers, pulled from the story.
A hydrogen bond is a molecular interaction that occurs when a hydrogen atom covalently bonded to an electronegative donor atom interacts with another electronegative atom bearing a lone pair, the acceptor. It exhibits partial covalent character and cannot be described as a purely electrostatic force, arising from charge transfer, orbital interactions, and quantum mechanical delocalization.
Hydrogen bond strength typically ranges from 1 to 40 kcal/mol, placing it stronger than van der Waals interactions but generally weaker than covalent or ionic bonds. Strength varies from weak bonds of 1-2 kJ/mol to a strong 161.5 kJ/mol in the bifluoride ion HF2-.
Hydrogen bonding gives ice an open hexagonal lattice, which makes the density of ice less than the density of water at the same temperature. As a result the solid phase floats on the liquid, unlike most other substances.
Linus Pauling credited T. S. Moore and T. F. Winmill with the first mention of the hydrogen bond in 1912, used to explain why trimethylammonium hydroxide is a weaker base than tetramethylammonium hydroxide. The description in water came in 1920 from Latimer and Rodebush, who cited the unpublished work of Maurice Loyal Huggins.
The double helical structure of DNA is due largely to hydrogen bonding between its base pairs, along with pi stacking interactions, which link one complementary strand to the other and enable replication. The bond between guanine and cytosine is much stronger than the bond between the adenine-thymine pair.
A water molecule can form up to four hydrogen bonds, two through its two lone pairs and two through its two hydrogen atoms. TIP4P simulations estimate an average of 3.59 bonds per molecule at 25 degrees C, rising to 3.69 at 0 degrees C and falling to 3.24 at 100 degrees C.
The term hydrogen bond is used for well-defined, localized interactions with significant charge transfer and orbital overlap, such as those in DNA base pairing or ice. The phrase hydrogen-bonding interactions describes weaker, more dynamic, or delocalized cases such as liquid water, lipid membranes, and weak C-H...O interactions.