We don't recommend biting the package to open the condom, either, for the reason you describe: it's too easy to cause a tear that way. Just opening the packet with your hands is the safest way.
No, you shouldn't keep condoms in a wallet. Some people buy little boxes or coin purses just for condoms, which is fine--they don't need to get stabbed by pens or keys in your pocket or purse. Remember that condoms should be kept at room temperature, and not be allowed to get too cold or too hot.
Yes, unrolling it and blowing into it is absurd and unsafe. All you need to do is remember that it should look like a little sombrero, a little hat: if you take it out of the package and place it on a finger, look at which way it will unroll--down the finger or the shaft of the penis. The best way to learn this is to practice with a few condoms and get familiar with them.
Check out this link for more:
A Simple Condom Primer
"And when the answer that you want/Is in the question that you state/Come what may..." - Coheed and Cambria, "Blood Red Summer"