Is any element base or acid?
Short answer is: Yes and no. It depends on what acid-base theory is applied.

Redox reactions like $\ce{Mg -&gt; Mg^2+ + 2 e-}$  are not usually considered acid-base reactions, but  over-generalized acid-base theories like Usanovich acid-base theory treat them as a special case of acid-base reactions.
Within this theory, $\ce{Mg}$ is relatively strong Usanovich base, $\ce{Mg^2+}$ is very weak Usanovich acid.

If we consider typical reactions by classical Broensted-Lawry theory:
$\ce{H2SO4 + H2O -&gt; HSO4- + H3O+},$
or $\ce{NH3 + H3O+ -&gt; NH4+ +H2O}$,
or by another classic - Lewis theory:
$\ce{NH3 + BF3 -&gt; H3N-BF3}$,
then atoms involved in acid-base interactions have the same oxidation number before and after the reaction.
$\ce{Mg^2+(aq)}$ is the conjugate acid to the conjugate base $\ce{MgOH+ (aq)}$.
$$\ce{[Mg(H2O)6]^2+ + H2O &lt;=&gt; [Mg(H2O)5(OH)]+ + H3O+}$$
$\ce{MgOH+ (aq)}$ is is then the conjugate acid to $\ce{Mg(OH)2 (aq)}$.
$$\ce{[Mg(H2O)5(OH)]+ + H2O &lt;=&gt; [Mg(H2O)4(OH)2] + H3O+}$$
$\ce{\pu{Mg}}$ has in all 3 species the oxidation number +2.