No, they just serve as a central point to match buyers and sellers so the buyers and sellers don't have to find each other themselves. They aren't making a market but they do get clearing fees.

No more like a broker. When you buy stocks through your broker, all the broker does is to pass on your order to the exchange, and to report when it was executed. The broker doesn’t take any risk, other than you not making a payment after you gave the buy order.

If the broker was a market maker, he would keep an inventory of that stock and your order would be filled by the broker directly. Who would then report and clear the transaction on the exchange.

Clearing doesn't mean buying and selling.

There's not really a great analogy, but the idea is that Goldman is on the hook if one of their customers can't maintain the margin/haircut.

More like match maker.