Oh, here are responses to your other questions.

A coaster brake is a wheel with a coaster brake hub. It can coast like a regular bike, and when you pedal backwards, it actuates a brake inside the hub. The harder you turn the pedals backwards, the more braking action you get. There is a side benefit in this where by putting your weight backward on the rear pedal, you move your body weight over the rear wheel, helping the braking action along.

Size of chainring (front sprocket) and cog (rear sprocket) is very significant. The greater the ratio between the former and the latter, the higher the "gear" as we say. High gears help you go fast but are harder to accelerate, decelerate and climb hills. Low gears are good for acceleration, deceleration, and hill climbing but limit your top speed.

On a fixed gear bike, I generally recommend a gear (or really effective rear wheel size) of 65 to 72 inches. Calculate gear inches this way:

G = F / R * 27

where

G is gear inches
F is number of teeth on front sprocket
R is number of teeth on rear sprocket
27 is approximate size, in inches, of your wheel

Since you have crazy hills where you are, you may want something smaller than 65 inches.