Is it permissible for the sheikh to recite the travel supplication (du'a al-safar) and the morning remembrances (adhkar al-sabah) over the microphone on behalf of the congregants on the bus, and is it permissible for them to repeat after him?

It is not permissible for the shaykh to recite adhkar on behalf of others, as the general rule in acts of worship is that no one performs them on behalf of another unless there is evidence to support it. As for him reciting the adhkar aloud and others repeating after him, there is no harm in it if the intention is for teaching. However, if the intention is for worship, then it is not permissible, as congregational dhikr was not transmitted from the righteous predecessors.