Sorry, I merged some stuff that conflicts with this. For the distances, I think it is ok to do what we currently do and let the input points determine the distance type. Is it really needed to get the distances in e.g. a lower precision than what you tree is built with?

For the integer type I agree it is a good idea to specify it. An alternative to this is to reduce the integer type to the smallest that could fit any index into the input data set. That would make things type unstable though.. But maybe with union splitting it is fine.