Ray tracing the next week: understanding Instances
There are two ways to 'translate' your object. The first is by moving each point of your object by the desired translation. The second is by translating the origin of your coordinate system. In this case it's the latter. Basically it turns out to be the same, whether you translate your object by a vector $\vec{t}$ or whether you translate your origin by $-\vec{t}$.

For 2) note that you only care about the intersected points (since that is what you use to compute the pixel color), so you compute the offset only when you need it. So yes, you do translate the origin of the ray at each intersect, it's the same as translating the object though (at each ray intersect), since $\vec{p}+\vec{t} - \vec{o} = \vec{p} - (\vec{o}-\vec{t})$.