The following come in no particular order. If you have Wayne Grudem's Systematic Theology, chapter 40 (pp. 788-809) deals with the doctrines of the perseverance of the saints and the assurance of salvation.
1.) Is assurance of salvation normative or exceptional in the Christian life?
2.) What are the differences between Catholics, Arminians, and Calvinists on assurance? What are strong points of each, and weak? What main problems (practically, not biblically) do each run into?
3.) Is assurance part of the essence of faith, or something entirely distinct that can be absent while true saving faith is present? This has been a huge question in the Protestant tradition, and is worth wrestling over. Think of biblical arguments. What problems do you run into in each direction?
4.) How do handle the tension between "I write these things so that you might know that you have eternal life" and "only the one who endures to the end will be saved"? That is, if we must endure to the end to be saved and not fall away, how can we have assurance until we have actually done it?
5.) What is the definition of assurance of salvation? How would Arminians and Calvinists define it differently?
6.) What role does the reality of false professors (Matthew 7:21-23, 13:1-30), not only now but on the last day, play in the doctrine of assurance?
7.) How can I know I am not self-deceived and actually have saving faith?
8.) What degree or kind of certainty are we talking about in the doctrine of assurance?
9.) What is the basis or foundation of assurance of salvation? How does it relate to the basis or foundation of salvation? That is, it is important to recognize that asking how I come to know God savingly, and how I come to know that I know God savingly, are two distinct questions.
10.) What passages of Scripture are particularly important and central for constructing the doctrine of assurance?