Some Questions related to Linear programming
Let me answer your questions one by one:


The solution of the linear program $\max x$ is $\infty$. This is an example with not finite optimum solution. This is the same as just having no optimum solution.
When adding slack variables, the optimum value remains unchanged. As an example, you change $x \geq y$ to the equivalent $x = y+z$, where $z \geq 0$.
You never minimize $3x+y=2$. What you minimize is a linear function, not an equation. Minimizing $3x+y$ and maximizing $-(3x+y)$ are the same.