Is this best done in a single day or multiple days?

Sharkstooth is attainable as a day climb. While the easier climbing and shorter approach make it easier to do in a day than some other climbs it makes an excellent overnight and with several of the Cathedral Spires and other climbs like The Petit or The Saber not too far it is an excellent place to spend a few days.

When is the best time of year to climb the Sharkstooth?

This is a climb that has different flavors in different season. Earlier in the Spring you may have snow that requires an ice ax and crampons making for a very classic mountaineering climb while in the fall that snow has melted and you can safely hike to the base in approach shoes for a pure rock climb. Both are equally enjoyable in our opinion.

Is this a good place for an introductory alpine climbing course?

With a nearby permanent snow field and accessible alpine rock routes it makes an excellent location to spend a few days working on alpine and mountaineering skills on actual climbing objectives.

Can this be combined with The Petit and The Saber

This is a really challenging ascent even for guides. We're happy to plan for a climb like this. Keep in mind doing it in a day is quite a physical feat and the logistics of getting from one formation to another can be critical in success just as much as the fitness of getting to them efficiently.