I'm wondering if is it possible to write a romantic dramatic book, and then write a second book that's a sequel but in a completely different genre, like a horror or psychological horror story?
Yes, it's possible. While changing genres during a story can leave the audience feeling betrayed - they expected one thing but got something else entirely - but changing genres between stories gives you a chance to let your audience know in advance, through (depending on the medium) trailers, interviews, the front cover, etc. This will lessen the shock, and give them time to adjust to the idea.
Some fans will invariably be put off by the switch; the more drastic the change, the more fans you're likely to alienate. The trick is to keep the core aspect of whatever made them like your first novel. To use your example, while the sequel may be a psychological horror, you can keep some of the romantic aspects by emphasising how the leads from the first book are still very much in love; that love can either help them get through the traumatic events of the story, and/or be exploited by who/whatever your villain is as part of those traumatic events.
A good example of how to do this is Aliens. The first Alien film was very much horror. Aliens, by contrast, was an 80s action movie, but it kept the horror elements from the first film and managed to blend the two together. The Alien Queen appearing from nowhere and graphically tearing Bishop in half? Horror. Ripley showing up in a power loader a few seconds later to fight her? 80s action movie. The fusion worked so well that Aliens is considered one of the greatest sequels of all time.
Possibly, but not without resistance. Anytime something is successful, both the publisher and the audience will demand more of the same. Your best bet is to do some genre-blending in a way that brings something old and something new at the same time. For instance, if your first book is romantic-drama, your second could be action-drama. People will stick with you if it was the shared elements that brought them to your book in the first place.
Harry Potter is a good example. Several of the books have different genre elements --middle-grade mystery in one, action adventure in another, war novel in a third --but the overall series stays grounded around YA fantasy.