How can a Muslim not rush the answer to his supplication and not abandon supplication, especially if he feels that his acts of worship have become a means to achieve this answer, and how can he rid himself of this feeling?

The supplicant's desire for their prayer to be answered is not blameworthy. Rather, what is blameworthy is the haste that leads to abandoning supplication. An example of this is the supplicant saying, "I prayed, but I was not answered." This haste is what prevents the answer. One must continue supplicating and entrust the matter to Allah Almighty, knowing that Allah knows best what is in the servant's interest, and that supplication is never in vain; either an evil is averted by it, or it is stored up for the Day of Resurrection. Striving in good deeds is a commendable matter, and it is a permissible form of seeking closeness to Allah through righteous action.