Can my Fiesta run without the turbo?

Technically, it is possible to run your car without the turbo, but long term it will cause damage, lower fuel economy, and wear out parts. you could remove the turbo, but it will feel like the car is towing an aircraft carrier behind it, and you'd need a mechanic shop to reprogram the engine tuning. So, technically yes. In practice, it would be best to get it repaired soon, sell the car, or swap to a non-turbo engine (but that could probably be more expensive than repairing the turbo).