Basement Insulation

The insulation in my basement runs only 75 cm (30 in.) down. I plan to finish the basement, which means tearing down the walls. Should I insulate them from top to bottom? If so, should there be an air space between the vapor barrier and the outside block wall?

It is always better to insulate from the ceiling to the floor. Even if the bottom half of the wall is below ground level, there will always be some heat loss without full insulation. The main reason that some newer houses are insulated only halfway is because it is less expensive to build them that way. Install a moisture barrier on the block to grade. Over that, install fiberglass insulation and a vapor barrier. Air spaces can transport moisture to the top and rot the floor. If air spaces are behind the studs, fill them with insulation.