My low coolant light and high coolant temperature light I are on
 

Just a quick question would this cause the engine light to be on to as well?

I would say if it is a 96 or newer that it is possible. They monitor so much more on the OBD2 cars. My car set a code because the thermostat was partially open.

My 97 just started using coolant. It does not take much of a drop in the level in the reservoir to trigger the low coolant switch. Top off the Reservoir and the light should go away. As for the service engine soon light, see what happens after you fill the coolant. Occasionally at startup when it is really cold outside the lights will blank until the thermostat opens. Always assumed it was an issue of thermal expansion and contraction