Where is the best place to sell my Mac?

Again, the most important thing is trust - you need to know the company will securely delete your data and pay you the amount you were quoted. If there's something about a company that makes you uncomfortable, you need to move on until you find one that feels reliable and trustworthy.

Speaking of data, I'm concerned about the security of my files on my Mac - how safe is it to sell my broken MacBook online?

Trusting the company you're going to work with is obviously the biggest factor. They also need to have the technical ability to securely delete your data even when the computer is completely dead. Beagle Brain has invested extensively in specialized Apple hardware interfaces which allow the connection and secure deletion of hard drives/SSD's even when your MacBook Pro or MacBook Air is completely broken and unresponsive.

Is it worth selling an old MacBook? Does anyone buy old MacBooks?

Yes, even older MacBook Pros and MacBook Airs have value. Again, you just need to make sure your Mac will be in good hands. It's good to research a company and make sure their reviews on Google and Facebook are positive.

What is my old MacBook Pro or MacBook Air worth?

We try to offer as much as we possibly can for your broken Mac. And we don't lower our offers arbitrarily because you got a spec a little wrong, or missed a small detail about the condition. It's extremely frustrating to not get the money you were quoted after you went through the trouble of sending in your computer, so we make a practice of paying people what we offer.