Let $K$ be a field. Let $X$ be a scheme over $K$. We denote by $K_s$ and by $\bar{K}$ the *separable closure* and the *algebraic closure* of $K$ respectively.
By base change we have the schemes $X_{K_s}$ and $X_{\bar{K}}$. I have the following questions.

- Is it possible that $X_{K_s}$ and $X_{\bar{K}}$ are isomorphic as schemes over $K$?
- Is it possible to have a bijection between $X_{K_s}(K_s)$ and $X_{\bar{K}}(\bar{K})$?

In the case I need, for example, $X_\bar{K}\simeq\mathbb{G}_{m,\bar{K}}^n$, where $n$ is a positive integer and $\mathbb{G}_{m,\bar{K}}=$Spec$(\frac{\bar{K}[X,Y]}{(XY-1)})$. Is some of the previous points satisfied in this case?