Not likely.
Check your battery for loose connections and check your alternator.
It is one of hundreds of things that could turn the check engine light on.
It could
Directly, no, but it's possible that the same root cause (something wrong with the electrical system) could make both warning lights come on.
could be low battery or loose connections
There is several things that can cause your battery light to come on. Go to your nearest Advance Auto Parts and have them hook up the battery and alternator tester because your alternator could be bad, or if you have a lot of electrical products such as a powerfull stereo system, gps, DVD player etc., you could be drawing to many amps for you battery and alternator to keep a charge
No, the battery light comes on when there is a problem with the charging system. More than likely the alternator is defective.
A bad stator causes the battery not to charge. That makes the battery light come on. Some other things that can cause the battery light to come on are corroded or frayed cables or connections or a loose/bad ground cable.
Yes it will
Very likely an alternator problem; if the alt is not working soon the battery would be drained and the truck would shut off.
Only the computer can tell what made your check engine light come on. It could be your battery. If your battery is bad, replace it and see if that solves the problem. If it does not, then you will have to connect your car to the computer and find out why the check engine light came on.
No, but it will cause your check engine light to come on.