What are the conditions for there to exist a convex hull on a set $X$ of points?
I know that there exists a unique convex hull for a set of $X$ points, but must no $3$ points be collinear in order for this to hold true or what are the conditions for this statement to be true?
Every set of $n+1$ affinely independent points has a unique convex hull referred as $n$-simplex. Now we must define what affine indepence is. The points $x_1,x_2...x_m$ are said to be afinnely dependent iff there exist real numbers $\lambda_1, \lambda_2...\lambda_m$ such that $\lambda_1+\lambda_2+...+\lambda_m=0$ and $\lambda_1x_1+\lambda_2x_2+...+\lambda_mx_m=0$. So if such $\lambda_i$'s do not exist then, as you say, there is no ambiguity and their convex hull will be the $m-1$ dimensional simplex containing them as vertices.