Note that the contribution from a positive charge is directed away from the charge. As mentioned, the electric field strength at the origin will be the vector sum of all these various contributions from charges at their various positions relative to the origin.
When the charge distribution is continuous, the vector sum has to be done using calculus (integration).

1.1 Prove that there is no electric field within a uniformly charged thin spherical shell. 

(This can involve a fair amount of work, e.g. see this video. Maybe better to just ask students to find the electric field strength for points along the axis of a circular loop of charge.)

??? Is this too much and too complicated? Concept of calculating potential and differentiating???

1.2 Derive the electric field strength for an infinitely charged line, a finite charged line, a uniformly charged semicircle, along the axis of a uniformly charged ring, and along the plane of a uniformly charged disk. (We will soon introduce Gauss's law that allows us to quickly derive some of these formulae.)

2. Electric Potential and Electric Potential Energy

As electrostatic force is conservative (i.e. work done by an electrostatic force in moving a charge from a given point A to a given point B is path-independent, unlike say friction), there exists a potential function \(V\) and associated potential energy \(U\). The potential energy of a charge \(q\) at a specific location is defined as the work done to bring that charge, from a location far far away, to that specific location. Such work done is the work done against the electrostatic force experienced by the charge  \(q\).