Following Riley's work,for each $2$-bridge link $K(r)$ of slope $r∈\mathbb{R}$and an integer or a half-integer $n$ greater than $1$,we introduce the Heckoid orbifold $S(r;n)$and the Heckoid group $G(r;n)=\pi_1(S(r;n))$ ofindex $n$ for $K(r)$.When $n$ is an integer,$S(r;n)$ is called an even Heckoid orbifold;in this case, the underlying space is the exterior of $K(r)$,and the singular set is the lower tunnel of $K(r)$ with index $n$.The main purpose of this note is to announce answers tothe following questions for even Heckoid orbifolds.(1) For an essential simple loop on a $4$-punctured sphere $S$in $S(r;n)$ determined by the $2$-bridge sphere of $K(r)$,when is it null-homotopic in $S(r;n)$?(2) For two distinct essential simple loopson $S$, when are they homotopic in $S(r;n)$?We also announce applications of these results tocharacter varieties, McShane's identity, andepimorphisms from $2$-bridge link groups onto Heckoid groups.