Does this helpful if you have self belief, commitment and confidence to face a problem with ease although you lack skills?

Yes it is very important  because if you don't believe in yourself, how can your boss believe you or your ability if your yourself have doubts in yourself.

Self-belief or self-confidence are thought to be the way that you feel about your skills, abilities, looks and behaviours. A person who has high confidence levels may learn things quickly, trust that they can complete tasks to a good standard or appear attractive to others. By definition, self-confidence means to have faith in or trust yourself.

However, confidence can also be described as the way that we project ourselves to others. We don't have to truly feel confident in our abilities, looks or capabilities in order to appear confident to others. Many people can portray an image to others of complete confidence while shaking with fear on the inside. This is a protection method used by many to cover up for a lack of self-esteem or other feelings about themselves that they would rather not acknowledge or show.

yes it does, as you're going to search and find a solution despite that you have no skills.

solutions are not necessarily from inside, it could be found outside 

yes it does. as you know "necessity is the mother of invention", when the need for something becomes essential, you are forced to find ways of getting or achieving it.