In this article, we generalize the $\mathbb{C}[\partial ]$-split extending structures problem of Lie conformal algebras to the super case. First, we introduce a unified product of a given Lie conformal superalgebra $\mathcal{R}$ and a given ${\mathbb{Z}}_2$-graded $\mathbb{C}[\partial ]$-module Q. This product includes some other products such as the twisted product, crossed product, and bicrossed product. Second, using these products, we describe and classify all Lie conformal superalgebra structures on $E=\mathcal{R}\oplus Q$ when $\mathcal{R}$ and Q satisfy some conditions.

This paper studies one-parameter formal deformations of Hom-Lie-Yamaguti algebras. The first, second, and third cohomology groups on Hom-Lie-Yamaguti algebras extending ones on Lie-Yamaguti algebras are provided. It is proved that first and second cohomology groups are suitable to the deformation theory involving infinitesimals, equivalent deformations, and rigidity. However, the third cohomology group is not suitable for the obstructions.

We introduce the class of split regular Hom-Lie color algebras as a natural generalization of split Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that every split regular Hom-Lie color algebra $L$