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,

[VavAlephVav]

The more I thought about what you said the more I decided that It really was running like **** all the time, it was really bad when it was cold and would straighten up a bit
once it was warmed up but still seemed to lack the go it had before. my gas mileage was **** and I could even tell the tone of the exhaust was different. It sounded like a pos Honda thpffpffpffpffpfffp

So it warmed up today and I took it back apart and sure enough

Thanks to my niece for the hot pink timing marks I made when I first took it apart.

I realize now that I had left slack on the water pump side. so even though the tensioner tightened up the other side when the motor was cranked over that slack became
one tooth off. lucky you can adjust the timing by getting the cam in place, then taking the belt off the cam gear and adjust the crank by hand while pulling on the belt.
without removing the Hbalancer or lower cover.

this time I double checked and got it right
Big difference now.

now I just have to wait three more weeks before I can finish my tune-up and maybe even get some struts

thanks