Will all the different types of mortice locks and latches fit my handles?

Yes. There are many different types of mortice locks and latches and the types will vary from different manufacturers. The only thing all sashlocks must have in common, irrespective of manufacturer, is the distance between the spindle hole and key hole. These dimensions are covered by British Standard BS5872. This allows you to choose any type of handles secure in the knowledge that they will fit any type of lock. (There are some special application locks which use unique handles but these are rare)