Hi Noob,
1. This looks like a Golden Motor kit. Golden Motor is known for their low prices and, more or less, reasonable quality (you get what you pay for...). The GM forums may give you an idea what, and what not to expect:
http://goldenmotor.com/SMF/
BTW, My experience with Yescom.com has been very good (quick shipping and very good packaging).
2. Range will typically depend on batter capacity (amp hours), terrain, average speeds, rider weight, and how much peddling you do. In your case this will probable fall within the lowest factory specs (which would seem to be well within your goals).
4. Your speeds with the GM kit should be about 26 mph or so (depending on battery condition (new, old, properly maintained, etc) , batt type (lead acid, Lifepo4, etc), and state of charge. BTW, 26 mph exceeds most U.S. regulations concerning electric bicycles. This isn't really a big deal as long as you use common sense (btw, always wear a proper helmet).
5. Watts = volts x amps. Higher volts generally = higher speeds while, higher amps = more torque (better hill climbing and acceleration)
6. Buying the parts "separately" will often result in slightly higher prices (unless you really "shop around"). Buy parts separately usually works well when you're assembling a vehicle with demanding and/or specific performance goals rather than for "saving money".
8. I highly recommend Lifepo4 batteries due to their superior performance and greatly reduced weight. These batteries almost always are cheaper in the long run as compared to sealed lead acid battery types. However, if you're truly restricted to SLA then, just be sure to buy a reputable brand from a reputable dealer. Keep in mind that SLA performance will begin to drop off just as soon as you start using them while Lifepo4s offer a relatively stable output during use (their performance remains pretty much the same through their use cycle). Hopefully other BF members can give you more detailed advice on SLAs...
9.The controller has a number of purposes which include (but are not limited to): control of speed (of course), regulation of maximum current (amps), reg of max speed (if equipped with a speed limiter for legal purposes), battery management (low voltage "cutoff" and high V cutoff), multiple speed settings (hi, medium, and low).
Good luck and good riding!