Is it permissible for a Muslim who fears Allah and avoids prohibitions to watch fighting and violence films that are free of adultery and women, or detective films, or those that contain veiled women, and can he combine work and da'wah in the future?

Your fear of Allah and your being affected by the mention of Hellfire are signs of goodness and faith. Therefore, you should thank Allah by staying away from sins and performing acts of obedience. Watching the aforementioned movies wastes time and money, and involves evil things such as nudity and music, and it decreases faith. Hence, they must be avoided. You must resolve to make sincere repentance and abandon procrastination. Calling to Allah requires knowledge of what you are calling to and the correct methodology of Da'wah (proselytization) with wisdom and good admonition. It is not a condition for the caller to be a scholar; rather, he calls with what he knows of the truth. Strive to seek Islamic knowledge so that your Da'wah may be based on clear insight.