Assuming Sirius is the same size as our sun, and at a distance of 0.1 light years, it would have an angular diameter of 0.3 arc seconds. If the corona is visible, it would occupy around 3 arc seconds.
If Sirius is 0.1 light years away, and the size of our sun, and the corona is visible, it would look a bit like this,
The image to the left is the suns corona. And, the image to the right is Sirius, from this video:
The precession of the Zodiac is 25,920 years, 1° every 72 years. If Sirius is similar in mass to our sun, using Kepler's laws, the semi-major axis of elliptical orbits is around 1000 AU. The two stars are at the present very close to apastron, the furthest they ever get in their orbit.