How to Fix a Frayed Cable on a MagSafe Power Adapter

Even if there isn't any obvious cable damage or bulging, the adapter could be failing. If the adapter is not one of the newer L-Shape Magsafe plugs, the need for a SMC firmware update is moot, but it's helpful to have the system up to date regardless.

Have you confirmed if a second, known-good adapter works on your Mac?

Updated: An SMC reset can also correct magsafe LED issues. http://support.apple.com/kb/HT3964

Yes they're compatible, however if the wattage of the charger is less than what the MacBook needs, it may not charge while the MacBook is running. That's typically only a consideration when you're using a charger from a smaller MacBook on a larger one. It shouldn't cause a burning smell or other malfunction.

If you're smelling burning, I'd get it checked out. Those things have been known to melt, particularly around the Magsafe connector, or where the cable meets the power brick. Check for frayed wires, etc. But I doubt it's related to using it on a different MacBook.