In this paper, we provide a comprehensive study of the structural properties of the transposed Poisson algebra W(a, −1). We classify several types of linear maps, including derivations, local derivations, quasi-derivations, and δ-derivations, showing that non-trivial δ-derivations exist only for δ = 1 and δ =1 . Furthermore, we describe the groups of automorphisms, local automorphisms, 2-local 2 automorphisms, and quasi-automorphisms. We also investigate Rota–Baxter operators of weight 1 on W(a, −1). Specifically, we classify operators that are homogeneous with respect to both the standard Z-grading and a Z2-grading, establishing a rigidity result for the latter case. Finally, we classify all W-compatible Novikov–Poisson structures, demonstrating that the associative product on the Witt algebra is universally compatible with its known Novikov structures.