How common is it for a child to have their canines congenitally missing?

Uncommon. True agenesis of canines is not common. Whatever happens more regularly is the impaction of canines either delaying or preventing their eruption into the mouth. It is also more common for people to have congenitally missing lateral incisors. A visit to the dentist will determine if the canines are truly missing. They can confirm it with an xray. Good luck.
Very Rare. Although I do not have statistics, very, very rare.
See a surgeon. See an ENT surgeon or plastic surgeon if the scar is over a year old. Even if it is not a year old, sometimes injections or laser treatments will help it heal better.
No, sorry. Sorry, but there is nothing to drink that will smooth out facial scars. If they haven't improved after a year, then you should see a dermatologist or facial surgeon for consultation as to what the treatments are.
Experienced surgeon. See a facial plastic surgeon or general plastic surgeon who does a lot of cleft lip surgery and get an opinion about what can be realistically expected from scar revision. Sometimes laser or steroid injections can do wonders.
Lateral incisors common. It is very common to be missing the adult lateral incisors. Many people have this.
Not common. Canines are more frequently impacted rather than missing. Your dentist can confirm with a panoramic x-ray. Most common teeth to be congenitally missing are third molars (wisdom teeth) and premolars (bicuspids). It is possible for a canine to be congenitally missing, just not common.