My name is ***** ***** I'd be happy to answer your questions today. I'm sorry to hear that this is happening.
Yes, your neighbor is responsible for both repairing the leak and cleaning up the mold, and any other damage caused by his actions. The law says that I, as a homeowner, have to make sure that my use of my property doesn't interfere with my neighbor's use and enjoyment of his property. I don't have a right to flood your property.
He's actually trespassing by directing the water onto your land. See Rosenblatt v. Exxon Company, 335 Md. 58 (1993). On top of that, he's creating a private nuisance, and you're allowed to ask him to abate the nuisance. If your neighbor won't fix the problem, you can actually sue and get a court order requiring him to move the downspout, on top a judgment for what it will cost to fix the leak and the mold. Both nuisance and trespass are intentional torts, which means you're allowed to ask for punitive damages on top of the cost of just fixing the problem. The amount you can get basically depends on what amount would be high enough to make him think twice before allowing something like this to happen again.
You have a few options here. One is to go straight to the courthouse and file a lawsuit. Alternatively, you could have a local attorney mail him a demand letter, explaining what you'll sue for if he doesn't take immediate action to fix the drain and stop flooding your basement. Or you could write a letter yourself, and send it via certified mail, which tends to get people's attention a little more than just a phone call or a conversation. Usually a demand letter contains a firm deadline for compliance, with a note that you'll sue if he doesn't do it. That might compel him to take action. But you don't have to do that first.
It's important that you are 100% satisfied with my courtesy and professionalism. Thank you.