What are the best ways to maintain your Toyota Corolla's engine?

I have just bought a Toyota Corolla and want to make sure that its engine stays in optimal condition. What types of maintenance should I regularly do for my Corolla's engine to ensure its longevity?

Regularly change the engine oil and filter according to the manufacturer's recommended intervals.

Clean and replace the air filter regularly to ensure proper air flow into the engine.

Check for any leaks or unusual noises coming from the engine, and bring it to a mechanic for a diagnosis.

Avoid excessive idling and drive at moderate speeds to reduce strain on the engine.

Make sure the engine is properly warmed up before driving, especially in cold weather.