In 1827, The Baltimore & Ohio Railroad experimented with sail powered railroad wagons. Twenty passengers sat in these cars and they proved to heavy for the wind to move. Early tests, with just two passengers were more successful, but the wind was just to unreliable for a vehicle on a fixed pathway. Wind powered skate boats, that could move over a frozen waterway had more flexibility to tack into the wind. They could move, even when the wind wasn't just right. Wind powered rail wagons could not do that and they were replaced with horse drawn wagons, when the first section of track opened in 1827.
Wind powered rail vehicles did find a small niche in the area of small track inspection cars. Charles Easton Spooner used one for his inspection trips on a railroad in Wales. A replica of Spooner's mid nineteenth century wind car was donated to the National Railroad Museum in York, back in 2010.

Yes, in 1826, George Pocock, an English inventor, patented his charvolant, which is effectively a carriage that is pulled by two large kites. The charvolant was apparently able to achieve speeds of 20 mph but was very difficult to control. The kites were also creating very large forces on the carriage which could suddenly push the carriage off the road or cause other safety issues. Pocock published a lot of these stories in his book: The Aeropleustic Art or Navigation in the Air by the use of Kites, or Buoyant Sails. He also mentions other uses for kite power, such as using kites to pull ships, but I don't believe that he was able to test any of them.

Certainly, and they are still around today. One is the 'wind buggy' (or 'kite buggy'), which is self-explanatory (wheeled vehicle using nautical-style sails or a kite to catch the wind). Who first invented this is disputable, but designs by Flemish engineer Simon Stevin, from the 17th century, are known. These reportedly functioned quite well, for recreational purposes, and were kept working until the 18th century (source: The Galileo Project). Modern designs are less grandiose.

Another is the 'ice yacht' (that counts as 'land', right?), which is an application of the same principle ('catch wind, will move') but with skids allowing for travel across ice. Since water resistance or wheel friction is no object, and far fewer materials are required to ensure flotation, these vehicles can achieve crazy speeds in the correct conditions, over 80 MPH (with unverified results even higher). Conventional sailing boats can be relatively easily retrofitted to travel on ice also - check out some youtube videos.