How do we write this correctly:
1 mm or 1mm?
With a space.
Although nobody is going to get confused if you don't. Some language style purists might get an aneurysm, but it's an occupational hazard.
OK, now I can be in peace.
Depends. Does the mm stand for millimeter or for micromanager? You ought to use the space, or lack of space, to differentiate between the two.
The micromanager being the one hovering close to you, with no space, right?
Yes, use the space.
And on a separate note, do not use italics for units (if you were curious).
Most variables and constants (single valued) are written in italics. (Vectors and matrix symbols are sometimes not though, but that's only to distinguish them from single valued constants and variables.) Actual numbers (e.g., 42) are not written in italics either. Nor are parenthesis and brackets. Also function names like sin() and cos() are not written in italics. And units are typically not written in italics. There may be occasional exceptions to these rules.
Separate names with a comma.