Group with all elements of order 2

Let $G$ be a group such that any $x\in G$ is of order $1$ or $2$, meaning that $x^2=e$ where $e$ is the neutral.

1. Show that $G$ is abelian.
   Now we assume that $G$ is finite.
2. Show that $G$ can be generated by a finite family.
3. Show that there exists a group isomorphism between $G$ and some $(\mathbb{Z}/2\mathbb{Z})^n$ where $n$ is a positive integer.

PS: We recommand the user to not use any bazooka like Fröbenius classification theorem (which says that any finite abelian group is isomorphic to a product of $\mathbb{Z}/p^i\mathbb{Z}$ where $p$ is prime) or Cauchy lemma (which says that if $p$ prime divides $\vert G\vert$ then there exists an element of order $p$ in $G$).