I'll answer your second question (on who pays the tax) first; and then address the first question (how the equilibrium point changes).
The reading assignment does not give much instruction on how to determine "economic incidence" in paying a particular tax. However, the following guidelines may help understand how to determine how a given tax (whether excise or sales) is allocated to the supplier and the demander. [Note, this is my understanding of the topic, and I'm not an expert.]
The starting point is the pre-tax equilibrium price (let's call it p), this is what the demander is willing to pay for a (given) quantity of goods that a supplier is willing to accept. After a tax is imposed, quantity becomes irrelevant in assigning the economic incidence of the tax.
After the tax, we'll have the post-tax supplier price (let's call it s) and the post-tax demander price (let's call it d). Note that
- one will be the post-tax equilibrium price, it just depends on whether a sales tax or an excise tax was imposed;
- d - s = [tax amount]; and
- d > p > s.
Consider the following breakdown of the tax amount:
(d - p) + (p - s) = [tax paid by demander] + [tax paid by supplier].
The logic behind these formulas centers around the fact that both demander and supplier were willing to trade at p. However, the demander now has to pay d instead and that the supplier receives only s (instead of p).
Now for the "other" question.
Since the problem is an imposition of a sales tax, the supply curve does not change (consider HW problem #1). The steepness (or flatness) of this curve will determine how the equilibrium price (and the equilibrium quantity) changes. To complete the problem, I would suggest first exploring what happens to the equilibrium point (and the corresponding variables of P & Q) in the four possible scenarios of combining "flat" or "steep" Demand curves with each of "flat" or "steep" Supply curves. Match the results back to what you've identified for these curves for Rachel & Jacob.
These four scenarios should also help you formulate how to answer the question of "who will pay most of the tax" in Jacob's and Rachel's scenarios.
I hope this has helped.