Can all systems be described by differential/difference equations?

NO. Many times stochastic or probabilistic dynamical systems can not be expressed by differential equation. Also many times differential equations are replaced by difference equation for numerical solution or for computer simulation.

1. What is the difference equation that describes the system?
2. How many types of differential equations can be defined?
3. Can we solve all differential equations?
4. Are difference equations differential equations?

What is the difference equation that describes the system?

Difference equations are often used to compute the output of a system from knowledge of the input. They are an important and widely used tool for representing the input-output relationship of linear time-invariant systems.

How many types of differential equations can be defined?

We can place all differential equation into two types: ordinary differential equation and partial differential equations. A partial differential equation is a differential equation that involves partial derivatives.

Can we solve all differential equations?

Speaking about ALL differential equations, it is extremely rare to find analytical solutions. Further, simple differential equations made of basic functions usually tend to have ludicrously complicated solutions or be unsolvable.

Are difference equations differential equations?

Difference equations are very much analogous to differential equations. Difference equations are more elementary, but differential equations are more familiar.