If I add custom points to plan by right click and "add position to flight plan" option, is it possible to move this marker via the mouse somehow. I only found the way to edit the LAT/LONG and no way to drag the point to another location. Is it possible?

Yes and even more. Click  on the toolbar to toggle flight plan editing. You can move, delete and add navaids or arbitrary positions to the plan. See here for details https://www.littlenavmap.org/manuals/littlenavmap/release/latest/en/MAPFPEDIT.html

Note that this is a click, release, move, click scheme and not click, hold, drag and release. This is bit different on purpose to allow scrolling with the keyboard keys while a navaid "sticks" on the mouse cursor.

You can also use the modifier+mouse clicks to edit a plan: Ctrl+Alt+Click adds (or deletes) a position into the nearest leg and Shift+Alt+Click appends (or deletes) the position to the end of the plan.

Alex

Super! Don't know what I'd do without LNM. Thanks for taking your time to make this wonderful tool! 🙂