Is an act considered insincere to Allah if it is done merely upon seeing someone else do it, such as giving charity or going for 'Umrah, and how can one distance themselves from showing off and dedicate their actions solely to Allah?

Emulating people of goodness and righteousness is not hypocrisy; rather, it is religiously commendable. Scholars have deemed it commendable to display good deeds for someone who is secure from hypocrisy, so that others may emulate him. This is based on the Almighty's saying: "If you disclose your charitable expenditures, it is well," and on the Prophet's (peace be upon him) saying: "Whoever introduces a good practice in Islam will have its reward and the reward of those who act upon it after him." Also, based on the hadith (definition) of Abu Kabshah al-Anmari: "A man whom Allah has given knowledge but not wealth, he says: 'If I had what this man has, I would do as he does.' So, they are equal in reward." This indicates that undertaking good deeds for the sake of Allah, by following the example of others, does not undermine sincerity.