Question

In which cases we shift the origin while finding miller indices

Answer 1

As rule of thumb you want to have as many intercepts between the indexed plane and your chosen axes as possible. Also you want to avoid having the entire length of one of your chosen axes intercept the plane.

Going the other way, from an index to a drawing, start from 0,0,0 and shift the orgin to 1 along any axis whose index is negative (has a bar over it).

There may be exceptions, but this should get you pretty far.