Can all types of computational problems be modeled as decision problems?
Yes.  Every computation problem can be viewed as computing a function $f:\{0,1\}^ \to \{0,1\}^*$: on input $x$, the algorithm outputs $f(x)$.

Here is a corresponding decision problem: given $x$ and $i$, determine whether the $i$th bit of $f(x)$ is 1.  If you can solve that decision problem, you can solve the original computation problem.

(Strictly speaking, you also need a way to decide whether the length of $f(x)$ is $i$; that can be addressed by defining the decision problem as taking inputs $x,i,b$; if $b=0$, then the problem is to determine whether the $i$th bit of $f(x)$ is 1; if $b=1$, the problem is to determine whether the length of $f(x)$ is $i$.)