Is root canal recommended for children of 3 years?

Pulpotomy . Similar to root canal for adults, it's done to remove infected tissues inside baby teeth to restore them and maintain the space for the permanent teeth when they erupt, which at least in three years for front teeth and 5/7 for back teeth.
Yes. Yes it is especially since the first teeth to be lost will be in approximately 2 1/2 to 3 years, for anterior teeth and 7-8 years for posterior (back) teeth, any infection needs to be gone for a long time. Infections in the area can affect the permanent teeth. If the tooth is extracted, then this can delay the eruption of the permanent tooth.
Possibly. Three year olds can have severe decay if they are allowed to sleep with a baby bottle... It's called baby bottle syndrome. Primary teeth are needed for mastication, speech, and to help guide the secondary teeth into place. Consult with a pediatric dentist.