Well, love is blind as they say... I know Ducky's sister Missy referred to Cyrill as "the marble man" because of his apparent lack of emotions, but maybe around Ducky he was a different person all together. Some of us put on a cold front to the world, sometimes because we're shy, or because we don't want to be hurt...but at home around our loved ones, we're very different people, aren't we? (Just thinking of Alix, and Queen Mary to name a few...)
If I remember correctly, they fell in love at Nicky's coronation, when Ducky was still married to Ernie. Since they were cousins, they would have been pretty close to begin with, but since D. was in the middle of a loveless marriage, maybe she confided in C. and he supported her. It was probably a combination of the heady excitement of the coronation, and the fact that she possibly felt admired by a man for the first time in her life. (While I love Ernie, I think everyone would agree it wasn't exactly a match made in heaven...) Maybe Cyrill was a very passionate man!
To answer your question about whether she was in love with Russia--I think to a degree, yes. It would have been romanticised in her eyes, from stories her mother (Grand Duchess Marie Alexandrovna) would tell her, and Ducky would have only been there for great family occasions and holidays, so then she would have seen Russia in it's best (and most exciting) light.