Few questions about dimensions

1) Is it possible to move a dimension value parallel to the dimension line without changing distance from dimension line?

2) Is it possible to set a different precision for each dimension (or for groups of dimensions), or do they all have the same default precision value?

3) Why positions of dim values changes to default (at center of the line) after I change drawing preference? Can I avoid such behavior?

1) Select the dimension by mouseclick, it gets highlighted. Now grab the dim value text at the small blue square and you can drag it anywhere you like.

2) No, only one dimension style can be set for the whole drawing, not individually.
    Maybe you can achieve the effect you desire by setting 'Linear zeros' to 'remove right'.  And also you can edit the value text with Modify - Properties, if it is worth the effort.

3) Unfortunately you can't avoid it. After changing drawing preferences all manual repositionings of dimension values revert to default.