Yes, writing a put is basically like getting paid to have a buy limit order on a stock. On your call question, I think you mean when you buy a stock and write a call at the same time, you could be hoping that someone exercises immediately to lock in a profit, but they may not until closer to expiration because they can sell with a time premium until it gets close to expiration.
ABC is trading at $100.50 and trending upward. Instead of buying it via a stock trade I sell an in the money put for $100 (for $3), which automatically executes and my basis is $97.5. Six months from now I want to sell the stock at $110. I sell an in the money call (for $2) and automatically gain two extra points.