If you use mm as unit, everything should be fine with the out of the box standard settings. Don't rely on the dots of the grid, they change their scale dynamically depending on screen zoom level.
Your problem may lie in the dimensions settings, but there are so many possibilities it's hard to tell from what you write. Instead of explaining everything I have made a simple template drawing for mm, scale 1:100 and A4, for LC 2.1.3, with not much changed to standard settings.
mm_1_100_a4.dxfIf you have different needs tell me your specifications and I can make a special version.