Does the Sharia call for a Muslim to trust in the talents and abilities that Allah has bestowed upon him, and to use them to overcome difficulties, while thanking Allah and acknowledging His grace, or is that forbidden, and should a Muslim rather disparage and reproach himself, as the predecessors did?

Self-confidence, after reliance on Allah, is Islamically mandated. The Muslim is required to have a good opinion of Allah, to be optimistic, and to strive to achieve his goals using his intellect and energy, as Allah Almighty says: "And when you have decided, then rely upon Allah. Indeed, Allah loves those who rely [upon Him]," and as He says in the Hadith (definition) Qudsi: "I am as My servant thinks of Me."

Lack of self-confidence is a type of helplessness that Islam does not approve of. The Prophet, peace and blessings be upon him, used to seek refuge from helplessness. The Salaf would accuse themselves of shortcomings in faith, even as they strived and resolved their affairs, relying on Allah. This is reliance [on Allah] by taking direct action on the causes, along with the belief that the results are by the permission of Allah.