You really ought to get a manual for your car. 20 bucks will get a Haynes delivered.
Yes your fans should come on. But with the size of radiator on this car, it ought never need them. (imo) Maybe in the summer.

You're coolant is full yes?
Have you checked the water pump? Run the engine and squeeze the coolant return, then release. You should feel a bit of pressure surge when releasing.

I would not run then engine at all if I could help it until this got resolved.