Is it a condition to renew the intention for every act—such as prayer and going to work—or is a previous, general intention sufficient? And does the supplication: "O Allah, make all my deeds sincerely for Your Noble Face" suffice in place of renewing the intention?

If the intention (niyyah) is meant as the intention to commence an act of worship, then it is a pillar that must be renewed for each prayer, and similarly for all other acts of worship. However, going to work does not require an intention for its performance to be valid. If the intention is meant as the intention to obey Allah’s command, then this is desirable (mustahabb) but not obligatory (wajib), and it helps in achieving sincerity in every action.