Uneven inflation of a new inner tube? I bought a new inner tube and when I tried to inflate it, the tube got unevenly inflated (check picture). This is the first time I'm installing a tube by myself so I don't know if this is normal. Do you think this is this a production defect, or did I do something wrong while pumping the tube? Can I fix it by myself?
Yes you did something wrong. You are supposed to put the tube in the tire and mount it on the rim.

If you inflate a balloon you will see similar behavior.  After you have stretched a tube IN the tire the behavior outside the tire will change slightly.