Orthogonal Sign Vectors

Let $A_n=\{(x_1,\dots,x_n)\mid x_i\in\{-1,1\}\}$. For $\vec x,\vec y\in A_n$ define $\vec x\cdot\vec y=x_1y_1+\cdots+x_ny_n$; if $\vec x\cdot\vec y=0$, call $\vec x$ and $\vec y$ orthogonal.

1. For $\vec x=(1,1,1,1)$, list all elements of $A_4$ orthogonal to $\vec x$. 2. Let $B=\{\vec x\cdot\vec y\mid\vec x,\vec y\in A_n\}$. If $m\in B$, prove that $m+n$ is even. 3. If $A\subseteq A_n$ with every two elements of $A$ orthogonal, find the maximum size of $A$ for $n=8$ and for $n=14$.