What does the Key / immobilizer light mean?

The car does not recognise the key, or the key fob battery is low.

How much does it cost to fix the Key / immobilizer light?

Typically $5 to $400 in the US, depending on the cause. A fob battery at the low end; a new programmed key at the high end.

Urgency:Safe to keep driving

If the car started, yes. If it will not start, the car has not recognised the key.

$5 – $400

A fob battery at the low end; a new programmed key at the high end.

A typical range, not a quote. Actual cost depends on the car, the shop and the fault.

Try the spare key.
Hold the fob against the start button or the marked spot on the steering column — most cars have an emergency reading position.