In chapter 7 of "The Great Gatsby," why does Gatsby fire his domestic staff? Who does he use instead?

First, let's answer the question about why Gatsby let all of his servants go with a couple of quotes from chapter 7:

“I hear you fired all your servants.” (Nick says,)

“I wanted somebody who wouldn’t gossip. Daisy comes over quite often—in the afternoons.”

"My Finn informed me that Gatsby had dismissed every servant in his house a week ago and replaced them with half a dozen others, who never went into West Egg Village to be bribed by the tradesmen, but ordered moderate supplies over the telephone."

So there you have it.  Gatsby ditched his faithful servants because he was afraid that they would gossip about his clandestine meetings with Daisy at the house.

Now, for the second part of your question, "who did he replace them with?"  Again, a couple of quotes illustrate this nicely:

"The grocery boy reported that the kitchen looked like a pigsty, and the general opinion in the village was that the new people weren’t servants at all."

“They’re some people Wolfsheim wanted to do something for. They’re all brothers and sisters. They used to run a small hotel.”

And there you go, answer number two.  He replaces his servants with some shifty characters that Wolfsheim owes a favor to.  They used to run a hotel, but don't anymore (probably because, according to the previous quote, they were lousy at keeping things clean and had bad manners.)  These "replacements" know how to keep their mouths shut, and they are not locals, so they have no one to gossip with.  Thus, they are of much better use to keep Gatsby's secret love-nest a secret.