Sub-optimal.  The protrusion suggests that the clavicle is not aligned correctly and that will not occur spontaneously, thus sending them home for monitoring is not likely to yield a suitable outcome.

Correct!  Most clavicular fractures are aligned and the arm held in a sling while the bone knits together. The length of time for healing varies with factors such as age and any other comorbidities. Healing is fastest in younger individuals compared to older. 

Usually surgery is not needed for a clavicle fracture.  However, if the fracture is complicated with multiple breaks (a compound fracture) or bone fragments have penetrated the skin, then some surgical intervention is needed. By itself, a clavicle fracture is not an emergancy.

There is no way to place a cast across the shoulder and chest, as this would restrict the ability to breath. Thus, plaster casting which is traditionally performed for extremity injury is not of use for a clavicular fracture. There is a close binding figure-of-8 split that is sometimes used, but most people find these generally uncomfortable, difficult to wear nonstop for six or eight weeks and can result in skin irritation and armpit odor (as the armpit cannot be washed while wearing).

Possibly!  If the fracture is complicated with multiple breaks (a compound fracture) it might require surgery to realign the broken bone fragments and to implant plates, screws or rods into the bones to hold the m in place during healing.