"Ag(s) reacts with none of the 4 (solutions of Ag^+2, Pb^+2, Cu^+2, Zn^+2}. So Ag(s) goes at the bottom of the table for now although there may be some metals below silver when you finish with the entire table.

Cu(s) reacts with (Ag^+ solution) so Cu goes above Ag ion. It is below the others, though, for it doesn't react with them. The reaction is Cu(s) + 2Ag^+ ==> Cu^+2 + 2Ag.
Likewise, Pb(s) replaces Ag^+ and Cu^+2 but not replacre Zn^+2. (We ignore the Pb/Pb^+2 for obvious reasons). So Pb goes above Ag but Zn goes above Pb. In the same way, Zn is above Ag^+, above Pb^+2, above Cu^+2, but we ignore reaction with Zn^+2. That is all of the information you can get from Reaction 2. But it shows you how it is done. Do the same thing for other reactions and build the entire table. I hope this helps you get started."

In other words,

the order would look like the following?

Zn
Cu
Pb
Ag

Actually Pb is between Zn and Cu although the information in reaction 2 doesn't tell you that (if I remember the question correctly). I assume that somewhere in the other tests you will have the info to determine exactly where Pb goes.

I found a pattern and I was wondering if it applies to all reactions.

The more times there is evidence of a redox reaction occuring for an element, the higher this element will be on the list?

Yes, based on the information given, the order would be Zn, Cu, Pb, Ag. This is because Zn reacts with all the ions (Ag^+2, Pb^+2, Cu^+2), Cu reacts with Ag^+2 but not Pb^+2 or Cu^+2, Pb replaces Ag^+2 and Cu^+2 but not Zn^+2, and Ag does not react with any of the ions. Therefore, the order from highest reactivity to lowest reactivity would be Zn, Cu, Pb, Ag.