How to align a workpiece in 4-jaw independent (off-center) chuck using a dial indicator and a sharpened point - [1]
Aligning tail piece to chuck - first use a very straight rod (such as cylinder rod) and then set adjustment screws on tailstock to move side to side. What about up and down? [2]
Indexing chuck - allows you to hold workpieces in a certain orientation, such as a pipe cross - at 90 degrees for 90 degree machining - [3]. This appears solved with CNC lathe/mill combination with multiple heads. Indexing chucks can also be automated so they turn the piece automatically - [4].

Notes

Lathe Chuck