No plural of "Eltern"
There is no singular of "Eltern". It is the plural word for "Vater and Mutter" (or whoever is parenting). "Der Elternteil" can translate to "the parent.
@Kelli 'Elternteil' is common but has a rather official touch. It is used a lot in juristic or political contexts but not so much in every day live. In the context you mentioned, you wouldn't use it. If you know which parent is with the child, you'd ask 'Wo ist dein Vater/deine Mutter?'. If you don't know, you'd ask 'Wo sind deine Eltern?' or indirectly 'Bist du alleine hier?'.
Is "Elternteil" a fairly common word? Would it be the word to use if, for example, you were at a playground and you asked a child, "Where/Who is your parent?".
The word "Elter" is virtually never used in everyday life. I guess a lot of Germans don't even know it exists. It is mainly used in scientific contexts. 'Elternteil' is far more common.