Map projection process for three-dimensional point cloud

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I have some points given in ECEF coordinates (or LatLongAltitude based on WGS84, which is interchangable in my understanding). Currently I am working on a mapping software which allows to visualize these points in maps. The current software version orthographically projects the points onto a plane, but future versions should support a wider range of map projections like Mercator and others. (It is not yet decided which exactly but the software design should be open to extension.)

From what I have read so far, a usual process for creating maps is

• project the 3D points onto the chosen reference ellipsoid which yields (2D) LatLong coordinates (in case of WGS84 ellipsoid, I could use my current LatLong and "drop" the altitude information)
  
• transform the LatLong coordinates into map coordinates (depending on the chosen map projection)
  

This actually is different from what we are doing currently: By first projecting onto the reference ellipsoid, the altitude is "lost". If then the projected point is transformed (e.g. with an orthographic projection) to map coordinates, altitude has no effect. In contrast, if the 3d point is directly projected orthographically, "altitude" (wrt to any ellipsoid) has effect on the output coordinates.

My questions are these:

1.) Is there any (practically relevant) map projection which follows the approach that we have currently implemented or do they "all" adhere to the two step process described earlier? (I.e., does the Altitude have an influence on the map coordinates?)

2.) Is it safe to assume that all points with the same LatLong coordinates (wrt any practically used reference ellipsoid) are on a straight line? (I know that depending on the choice of geodetic or geocentric coordinates, these lines for different LatLong may have a common point or not, but that's not too important for me.)



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