Answer
No
Yes
Work Step by Step
A continuous function needs not be differentiable as differentiability depends on other factors such as whether or not the function has a sharp turn at the point under consideration, or whether the tangent to the function at the given point is completely vertical.
For example, take the function $f(x) = |x|$
In the attached image, notice how the function hits a sharp turn at $x = 0$.
Here, the function is continuous but not differentiable.
A differentiable function is necessarily continuous.
