How can $\underset{\mathbf{x} \in \mathbb{R}^2}{\text{min}} \frac{1}{2}\langle x, Ax \rangle + \langle B,x \rangle + c$ be unbounded

Question

I have a few questions regarding the optimisation problem.

1. I was told that when A is semi positive definite (implying the function is convex) and A is symmetric, $\underset{\mathbf{x} \in \mathbb{R}^2}{\text{min}} \frac{1}{2}\langle x, Ax \rangle + \langle B,x \rangle + c$ optimal value may be unbounded. How can this be so when it is a quadratic? And apparently if it is bounded, there could be many optimal solutions? How and could any examples be provided? Can this be extended to $\mathbb{R}^n$?

2. When A is positive definite, I believe the function is strongly convex but I can't figure out what scalar of the identity the hessian (which is A) would be greater than.

3. When A is indefinite, the function becomes non convex. Would this mean it is always unbounded below?