lacks power only when cold, poor mpg, verify timing Options

[VavAlephVav]

So I've only had the car a little while and this is the first time I've been driving it when its Butt cold outside. 5*F/-15*C
when the motor is cold it hesitates more than I've ever seen it and downright seems to have no power up through 3000 rpm or so.
of course this motor warms up fast so it only does it the first couple of times I shift and then it goes away, except that my gas mileage is down to like 22mpg or so.(although I was only getting 26 or so before)
OK, so I understand that all motors act funny when its cold, but this one seems worse than it should be.
I did just replace the water pump... and I know I turned the crank with a wrench after installing the belt and checked the marks, but I am paranoid that somehow when I
adjusted the tensioner it got off by one tooth or something. sadly you have to do the biggest part of the job to get the motor bracket off so that you could get the top timing cover off just to verify the mark and see if its timed right or not.
I'm tempted to drill a small hole in the timing cover so that I could see the cam mark and verify it before I spend the whole day taking the motor apart and maybe find out that the timing is ok.

I'm wondering If you check the ignition timing with a timing light will that verify the valve timing by the timing belt or no?
also I need a whole bunch of tune up stuff, so far I have new cheap copper plugs but I still need stuff like wires, cap/rotor, fuel filter, IAC, and probably an EGR even though I have not tested it. and my air intake hose is held together by ducktape
and is there a certain period of time the computer needs to relearn after its been unplugged a while? I've only gone through one tank of gass since I did the water pump.

any insight you guys have as to how to check and be sure before I tear the whole thing apart would be appreciated,

[DeviantCorndog]

First check your spark plugs for signs of fuel/carbon fouling that would be a good indicator if your timing is to advance. Which is is indicated by dry, black, fluffy deposits on the spark plug electrodes. Also Fuel fouling is most often caused by an air-and-fuel mixture that’s too rich. However, a blocked exhaust or faulty valve can also cause fuel fouling. If the problem is severe, you might be able to smell fuel on the spark plug.
A weak ignition can also cause fuel fouling. For instance, if the spark is weak because of a faulty cable, electronic module, coil, condenser, or because of weak points, a plug can become fuel-fouled. In addition, if the spark plug is too cold for that particular engine, it may become fuel-fouled.
If a cold plug is installed in a cool-running engine, heavy carbon deposits form on the electrodes, making it difficult for the spark plug to fire. When the plug is in the correct temperature range, the heat from combustion burns the byproducts of combustion off the electrodes and keep them clean without causing them to over-heat.

And Considering you just got your car I might be a good idea since your where is very cold to make sure you have the correct oil/trans fluid weigh. No really good way to test that except to change it to be sure, or just check and make sure you are at full capacity for both of them whichever is a cheaper route. Me personally would go with a good set of spark plugs because they are fairly inexpensive and last a good while. When you do change your plugs or at least check them make sure you know which cylinder they came from and you can see if a specific cylinder is having trouble. Try and take a few pictures..and I might be able to give some more input if you need.