The cheapest would be something like the Tap A Draft system, the easiest would be a simple soda keg setup. The TAD system will easily fit into a refrigerator, the soda keg requires a spare fridge.
I steep the carapils for 15 minutes. I don't know about lagering with kolsch yeast, if I had the patience and the fridge for lagering I would use a bavarian lager yeast.
If you use a smaller pot that gets at least half full when mashing then you should be fine following deathbrewer's guide. I also put my pot in an oven that has been pre-heated to around 150 F to prevent heat loss.
Sounds like it's doing great, but don't get impatient and bottle too soon. Let the yeast clean itself up and for the beer to clarify some more even if the gravity reading is stable. I like to wait at least 7-10 days before bottling (even longer for bigger beers).
To keep things simple go with a dry yeast (either the Danstar Nottingham or Safale us-05), its easier to work with, just sprinkle it on the cooled wort. The yeast fuel and alcohol boost is not necessary. Dry yeast should be fine without a cold pack.
Their priming sugar will be fine for...
If you have the means to calculate your target original gravity and IBUs, you can use this chart http://www.brewsupplies.com/hops-gravity.htm to determine the balance between bitterness and maltyness
I would suggest using about 3 pounds of DME in 1.5 gallons, then reducing this till it gets thick. Then add this "caramel" to your boil. Plan on taking 2-3 hours to reduce to the proper thickness.
This reduction (or kettle caramelization) is what gives the wee heavy its characteristic dark...
With 8 lbs. of extract you should definitely have better than 1.016 OG no matter how much water you add post boil (assuming you are doing 5 gallon batch). I would suspect a misread of the hydrometer first.