How & Why Devis Durga, Lakshmi & Sarasvati are worshiped in their child forms? 

We know that Krishna is worshiped as a child with the names, Mukunda, Gopal, etc.

Devi Durga, Devi Mahalakshmi and Devi Sarasvati are also worshiped as children in many parts of India.

Devi Durga's child form is KATHYAYINI.

Devi Lakshmi's Child form is BHARGAVI.

Devi Sarasvati's Innocent form is AYANA. 

It is the mercy of these three devis to appear as children because, the childhood form is innocent and liked by the devotees with the child's innocent hearts.

Innocent people worship innocent forms of Krishna, devis, etc.,

Since Krishna and the devis like to have the devotees with child-like hearts, they appear as children forms.

When the devotees have child-like hearts, they won't have Kama, Krota, etc and they will have pure heart.  That is why, the devotees should have child-like hearts.

When Krishna and devis are in their childhood forms, they are innocent.  So, the devotees can easily convince them with their prayers and penances.

That is why, Gopis too worshiped Parvati as Katyayini devi.

Interesting.  Isn't it?