Can an omnidirectional antenna be used with a directional one?
A directional antenna is always preferable to omnidirectional. Both for transmitting and for receiving. But, as you say there may be factors that preclude using a directional antenna. For example, for portable (especially hand-held) use, a directional antenna may be to unwieldy, so a whip or "rubber duckie" antenna is typically used.  Or if you don't know the direction of the communication, a directional antenna can be a liability.

If your mobile end knows what direction the fixed location end is, then you would benefit from at least using a directional antenna where you KNOW the direction.

A directional or omnidirectional antenna can be used with any type of antenna at the other end.  Some VHF and UHF communication use polarization where the receiving antenna should be using the same polarization (vertical, horizontal) as the transmitting antenna