I have inserted a line into a text document and have a few questions. First, I need to make sure it is horizontal.
Press the Shift-key while creating the line. Then it is horizontal.
Or use Ctrl + Click on icon. That inserts a default line in the middle of the window. That one is horizontal too.
Is there a way to ensure
it is perfectly horizontal and won't print with the offsets for diagonal placement? I am unable to see if it is perfect.
Use item "Position and Size" from the context menu of the line. That dialog has a tab "Rotation", where you can verify that the rotation angle is 0° and correct it if necessary.
I have done this in the
past using tab spaces with a right justified tab, but LO won't underline tab spaces.
You will not get a line but a sequence of underscore characters. If it does not work for you, than perhaps the fill character is not set for that tab stop? You find the setting in the page "Tabs" of the paragraph properties dialog.
Second, I need to move the line up slightly. If I select the line and tap the arrow keys, it jumps an entire text line or more (it looks greater than the font size for that line, e.g. 12 pts).
The smallest movement with arrow keys is achieved, when you press the Alt-key while using the arrow keys. You get movement by pixel then. If you use a high zoom in addition, the movement is really tiny.
For an exact position use the above mentioned dialog "Position and Size"
It's as if it is
snapping to a grid.
Such might be. Is option "Snap to grid" enabled? You find the setting in menu Tools > Options > Writer > Grid, in the upper part. Clear the checkbox.
I want to be able to move the line in very small
It would be good, if you describe the purpose of such line. There might exist a totally different solution for your goal.