The first thing for making the map make sense on a sphere is to remember that for a rectangular map, the top and bottom lines are actually points (the North and South poles). Therefore, the entire top and bottom edges of the map need to be either all continent or all ocean.

Faults are usually great circles on a globe. They do indeed become sine waves on the map. I think it's rather that they're not normally so "crisp" on continents.

Major transform boundaries - where one side moves sideways with respect to the other - are not too common on continents. The San Andreas is the best known; others include some around Turkey and one through New Zealand.