When creating line objects the Advanced Digitizing window shows you distance (d), angle (a), x coordinate and y coordinate.
To use it, switch on both the Advanced Digitizing panel and toolbar and click the icon for 'Enable advanced digitizing tools' when you are editing
I'm not sure whether you are comfortable using the python console, but here is a short script I wrote which should do what you want (one row of points at a time). In case you are not familiar with running scripts in the console, open the python console, click the 'Show Editor' button, and paste the following code into the editor.
Note: Before running the ...
I do not think this is possible in ModelBuilder.
But you could create a model that :
convert the line vertex to point
add XY (and if needed ZM) coordinate to the newly created point
select some of the point
Export a table with the coordinate you're after
You have mentioned that you are using "Regular Points" to create points arranged in lines over an area.
You could create another layer with "Regular Points" with half the vertical spacing of the first layer. Pay attention to the extent of both layers.
Then you could use this new layer to snap new points on the first layer to decrease the spacing.
If you're having trouble getting the little cross to pop up on the segment you want to add the node to, check your snapping tolerances. Mine were too high, making it impossible to get it on shorter segments. Go to settings > options > digitizing > snapping > "search radius for vertex edits" and set it to something like 10 pixels. Mine was set to 100 map ...