Bike tires loose air much faster than car tires; they're at higher pressure and have much lower overall volume. Many road-bike guys check 'em daily. At least weekly.
A good guage is a necessity. Very low volume of air in the tire means you can overinflate (and pop!) them pretty easily with a gas-station pump. Those guages are notoriously inaccurate.
Best just to spring for a decent floor pump.

I've found with a new bike it takes at least a couple of weeks for those new cables to start to stretch. Wait till the shifting starts to get "clicky" and take 'er in. (or learn to make these minor adjustments yourself)