Does everyone who does a good deed in this world feel happiness and a sense of relief, even if it's for show and not seeking the pleasure of Allah, such as helping an old man to gain people's approval and set an example for others? Is this act considered forbidden and does it prevent the feeling of happiness? And does this apply to both Muslims and non-Muslims?

If a Muslim displays virtuous conduct, such as respecting elders, with a worldly intention, there is no sin upon him, but he misses out on the reward. However, if he adds the intention of seeking Allah's pleasure, then he will be rewarded. As for pure acts of worship, such as prayer, intending to show off to people through them is forbidden hypocrisy (riya'), which is minor shirk (definition). Immediate happiness may be attained by both Muslims and disbelievers due to worldly deeds, and the disbeliever is recompensed in this world for his good deeds. As for true happiness, it is only achieved through faith and righteous deeds, in confirmation of His (Allah's) saying: "Whoever does righteousness, whether male or female, while he is a believer - We will surely cause him to live a good life."