Scale of measurement flip (horizoltal and vertical) and staying at the job origo

What do you mean by this? Other than homing and origin location, in normal use nothing should be mirrored and you should have no functional difference in how LightBurn operates.

As far as I know this cannot be done. It seems on Ruida machines that home location and origin location must be the same.

First make sure that what you think is happening is actually happening. Typically the machine will return to its user origin. This is likely to be at the same location as absolute origin unless you’ve pushed the “origin” key on your panel somewhere else. So it may not be set to return to the absolute origin but just seems that way.

You can change whether it goes to user origin or absolute origin after a job. Check out this Topic.