Concerning the first question, this identity is due to Poincaré [1], who showed that $W(t)=\log (e^X e^{tY})$ solves the ODE
$$W'(t)=\frac{\text{Ad}W(t)}{1-e^{-\text{Ad}W(t)}}(Y),\;\;W(0)=X.$$
The identity in the OP is the solution to first order in $t$. It holds generally, you don't need $[X,Y]=sY$.

[1] H. Poincaré, Sur les groupes continus (1900).