They are worn in mourning, as a sign of respect for a deceased person that the players knew.
According to the New York Times article (see related links below), the armbands are nothing more than the current fashion trend with the purpose of showing off their upper arm definition. Wearing the armbands (in many cases wristbands moved up to the upper arm) has no medical or performance benefit.
That certainly is possible. However, the shoulder pads that football players wear are made to come down over the upper part of the chest. So a player could possibly have the wind knocked out of him by a hit to the upper chest but that would be more common with a hit to the lower ribs or midsection where there is no padding. Click on the 'Football Player's Padding' link on this page to see a picture of how a player looks with all of his padding on.
There are 2 resistance bands that are used to work the upper body.
Is really what makes you comfortable, Most players wear it on the upper jaw.
If you are looking at the jersey it is on the upper right hand side, if you are wearing the jersey it will be on the upper left hand side. This is true for every NHL team with the exception of the Detroit Red Wings, where the "C" is in the upper left hand side if you are looking at it, and the upper right hand side if you are wearing it.
To protect shoulders, upper chest, ribs, upper thighs, head, and abdomen.
You can not run without moving your upper limbs in contra lateral positions to lower limbs. (Try to run with upper limbs tied to your body.) Importance of running in football needs no comment. Also imagine the goalkeeper not using his upper limbs!