I'm just starting to study chemistry so sorry for the probably obvious question to you, guys. According to the definition of molecule in Wikipedia:

A molecule is an electrically neutral group of two or more atoms held together by chemical bonds.

According to that definition, I assume that parts of the molecule could be theoretically connected just with the h-bonds. As far as I understand the example of that case is DNA two strands of which are connected by only h-bonds (though many and many ones).

According to Khan Academy:

When atoms combine by forming covalent bonds, the resulting collection of atoms is called a molecule.

And now, as a newbie, I'm a little bit confused with all of that. So, could you help me with the following questions:

1. Is that true that two strands of DNA do not have covalent bonds to each other and connected only with h-bonds?
2. If the p. 1 is true could parts of molecule be connected only by h-bonds by definition?
3. If the p. 3 is true then why DNA is a molecule but two water compounds (H2-O***H-O-H) are not?