I wonder if I can do simple arithmetics with coordinates. Can I do substraction of coordinates like 2.570801 (lng) 46.89023 (lat) / 17.424316 (lng) 55.15377 (lat)?! Or will that get messy without a CRS?!
Yes, you can do that. You might want to look into spherical trigonometry for that. Though i personally find it much harder to interpret the results this way and would project the data into a metric-based crs like utm before doing any arithmetics.