Schwinn Graft Pro...How do I adjust the handle bars

loosen of the handle bar stem from the front forks and turn to square to the wheel then re-tension the bolt/s

These are certainly not racing style bars; but the modern, hybrid riser handlebar.

They will not sweep back toward the rider as much as a beach cruiser handlebar; but could be adjusted rearward to come closer to the rider. They definitely allow for a more upright riding position than many other handlebars though.

http://www.sheldonbrown.com/handsup.html

A major limitation is the steerer tube length. No matter how many times you cut a steerer tube it won't get longer.

Getting Riser Bars or simply flipping the stem over or getting one with a different rise and reach might give you the added height you need. If you LIKE the handlebars, the stem is the best and least-invasive option as most new ones come with front loaders (detachable front caps) that allow replacement without stripping components off one side of the handlebar. In minutes a Bicycle Shop could swap any number of them onto your bike for you to try.

A reputable Bicycle Shop would have fit the bike to you before you took it home.

Most likley a rear drailleur issue. Try to turn the adjustment screw at the handle bar end where the derailleur cable goes into the grip. This is a fine adjustment screw for the drailleur itself. It will allow mirco adjustment of the cable to line the derailleur up perfectly so the chain stays in place

You could get instant opinionated answers from people who have experience with it if you just go into any search engine with "Schwinn Graft Pro review".

It looks more like an entry level cross country bike to me. How many other good bikes sell for as little as $350 and have disc brakes on only the front and find it necessary to point out such standard features as quick release parts?

That cap never needs to be removed. It is simply for adjusting the preload on the headset bearings while the other bolts on the stem secure that adjustment.

Hit the search engines with "threadless headset adjustment" for many explanatory videos.

Don't you mean SCHWINN? They don't usually make a manual for a specific model unless there is something unique about it.

http://www.schwinnbikes.com/support/owners-manuals

Since there is nothing unique about that Schwinn versus any other bike you could also look around the web for specific parts and procedures.

For example...

http://www.parktool.com/blog/repair-help

Probably. Getting Riser Bars or a riser stem or simply flipping the stem over or getting one with a different rise and reach might give you the added height you need. If you LIKE the handlebars, the stem is the best option as most new ones come with front loaders (detachable front caps) that allow replacement without stripping components off one side of the handlebar. In minutes a Bicycle Shop could swap any number of them onto your bike for you to try.

Detailed advice...

http://www.sheldonbrown.com/handsup.html

In order to raise the handle bars, you will need a hex key. Put it into the hex indentation at the top. Turn it left to loosen it. Then raise the handle bars to the desired height.

I am not sure which question to answer, so I will try both.

raising the handlebars, loosen the stem bolt 4or 5 turns, (this is the bolt on on the top of the handlebar stem). Tap the stem bolt with a hammer, the bold should drop down and the handle bars should fall loose, adjust as needed, then tighten the stem bolt to set.
Please note, there is usually a limit line on the stem, do not raise bars above this level as iy will make the handle bars unsafe and could pull out or break off.

second question, Child seats ar very adaptable, an will fit most bikes. Be sure to use all the necessary hard ware and safety guards. for you and your passenger.
Try to get the seat set up as low as possible as the higher the seat the higher the center of gravity. It will have less effect on handling characteristics if you keep the seat low.

I hope this is of some help.
Ed