1. Can functions with roots and surds be differentiated?

Yes, provided that they are written in index form first.

2. Why is the derived function of a function such as f(x) = c, where c is a constant, always 0?

Because f(x) = c is a horizontal straight line whose gradient is 0.

3. Is it possible to differentiate an expression with brackets in?

There are ways to differentiate with the brackets still there, but at this level it is simpler to expand them first.

4. Is it possible to differentiate every function?

Some parts of some functions are not differentiable.

e.g. In an absolute value function or a piecewise function if the graph is pointed the function is not differentiable.

If a particular function is not continuous i.e. You have to lift your pen off the paper when sketching the graph, say with asymptotes,then it cannot be differentiated at that point.