I started a project with CRS WGS 84 /Pseudo Mercator and I created a shapefile including point features in different locations around the globe. I have been already working on that for a while and all the operations done so far to measure distances and areas have worked fine enabling "on-the-fly" mode (eg. drawing poly-lines connecting these points, measuring the length of those poly-lines, density of the points, etc).
Now I need to export XY coordinates of the points to use them as an input for a tool external to QGIS (csv, xlsx, or similar formats are fine), but I noticed that the values of XY coordinates do not reflect the actual ground distance between points at each location. For example, for 2 points located in Iceland being 600m away from each other on the x-axis, the difference of X coordinates is 1400m because of my initial choice of CRS. What I would need is XY coordinates relative to the location of each subset of points (eg, with origin on one of the points itself) reflecting the actual ground distance. Note that the geographical position of the points is not important anymore.
Is there a way to extract those coordinates at this point, even with a poorly chosen initial CRS, or to reproject my point shapefile to a more suitable CRS, in order to be able to work with those coordinates?