[yuheng_wu]

Does HCHO have a hydrogen bond between H-O or not? If not, why? A hydrogen bond is always between a H and F/N/O so in this molecule there should be one if my reasoning is correct.

[AWK]

Depending on the level of chemistry, different classifications of concepts are clarified or expanded.
At the lowest level of understanding of hydrogen bonds, it is believed that such bonds are formed between a hydrogen atom bound to a heteroatom with another heteroatom, e.g. ~OH ... O~ .
As the details of the crystalline structure of chemical compounds are studied, the concept of hydrogen bonding is slightly expanded, e.g. bifurcated hydrogen bond, CH hydrogen bond, and even more - because how, for example, to explain the presence of a hydrogen atom from chloroform exactly above the center of the benzene ring and the H-C bond perpendicular to the ring plane?
But you still have time to understand such details.

[chenbeier]

On basic level formaldehyde has C-H bonds. There is no hydrogen bond to oxygen. Under normal condition boiling point is -19 ° C also a gas.  There are only adducts with water available to max. conc. 32% . HCHO + H₂O => HOCH₂OH. This has Hydrogen-Oxygen bonds.