Could you have sand pipes like water pipes?

Tricky for sand, most grains of sand are 'sharp' they will lock into each other and form jams in the pipe unless you have some fluid (eg. air or water) carrying them along. There are types of sand with smooth polished grains which flow more freely (eg desert sand) but these aren't used in construction so there isn't much effort into moving it around.

Smoother particles like grain are routinely moved around in pipes.

The other problem is how to pump them. Pumping requires a fluid that you can compress in the pump so there is a pressure difference that transfers force to other particles. Although it's easy to lift particles to the top of a pipe and have them flow down, it's less clear how you can pump solid sand particles up without using some carrier fluid like air or water.

To pump the grains up, the Archimedes Screw is used in agriculture. This should also work for sand.

Yes! If you go back to see how the old steam locomotives were built, one of the domes on the steam engine held sand that flowed down through a pipe were it ended near the tracks in front of the front drive wheel. The sand was added to provide traction between the steel wheel and the steel track. There was also a washer that washed the sand from the tracks just after of the rear drive wheel. For the sand to flow, it needed to be completely dry. The railroads had a house, not surprisingly called the sandhouse, where the sand was dried by heating it using a coal stove.