Is it ok to use a 45w mag-safe charger instead of the 60w mag-safe that came with my MacBook Pro 13?

Yes, you can use a 45W MagSafe charger with your MacBook Pro 13, but it may charge more slowly than the original 60W charger, especially during heavy usage. While it should be sufficient for basic tasks, using a lower wattage charger may not provide enough power under demanding conditions. For optimal performance, it's best to use the charger that matches the wattage recommended for your device.