How does radiator fluid leak into the engine?

Coolant from the radiator and engine oil are supposed to be separate and never mixed. If they are mixing, you probably have a problem with either the engine’s cylinder head gasket or perhaps an oil cooler that uses the radiator coolant to do its thing.

If the oil has water in it (or vice versa) don’t drive the car any farther as the diluted engine oil can destroy the engine. Similarly, if the coolant is escaping into the oil, you might find there’s no longer enough coolant left in the radiator to prevent the car overheating., That can destroy an engine, too.

As for a warranty claim, a blown head gasket is a bit of a grey area. You may have to prove that the gasket blew of its own accord, rather than through you continuing to drive the car with an overheated engine or some other form of abuse.