Hey, a good question finally. And the answer is no.
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In a world where trade is vital to all countries, a country that has nothing for sale will soon go bankrupt.
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We’ve become a nation of servants. No, it’s not. We’ve dissolved the production industry in this country to appease the wealthy who don’t want to pay a fair wage. Instead they move overseas to build sweatshops and exploit people who are too desperate to fight.
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You mean is a "free market" sustainable? Yes. Obviously it is. If a maid could afford a maid, the former would not be a maid.
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No, manufacturing is the foundation for every successful economy.
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A total service economy would be impossible to maintain. Europe comes closest to trying, but even then most of their countries have some major industry. France has Airbus, Germany has automotive, Italy has…tourism, and Ireland is becoming a center of scientific research. But then, they have been enjoying 10% unemployment levels with enormous tax burdens for some time.

ADD: Interestingly, in Homer’s Odyssey, Odysseus returns home and stays with his slave Eumaeous, who has himself saved up enough to purchase a slave for himself. So maybe a maid could hire a maid.
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No its not sustainable.
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Not service ONLY. But we don’t have a service only economy. Who manufactures the cleaning products the maid uses? Manufacturers.
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Only if you want butler to be the highest attainable job in the country.
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The answer is yes, in spite of the widespread misconception that such a scenario wouldn’t be. Automation is rapidly rendering human input in the primary and secondary sectors superfluous, and it won’t be terribly long until the provision of services is the principal occupation of man.

Quite some time ago, the same sort of sentiment existed, however it was instead focused upon agriculture. Now, due to technology, only 2% – 4% of the population is engaged in that pursuit.
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Of course it is. There’s a lot of negative talk about service jobs. I think this is a fundamental misunderstanding of economic principles combined with fear of the new and unknown.

Nearly every parent in this nation, and in every industrialized nation, wants his or her children to be employed in a service occupation: lawyer, doctor, accountant, etc. We all want our children to be professionals, not slaving away in factories. Yet Americans love to complain that these industrial jobs are leaving. If other nations can do these jobs for less money, they should do these jobs for less money. It benefits our economy to have cheaper goods. It benefits their economy to make these goods for us.

The ultimate fear, I think, is that we will not have the jobs here so that Americans can afford the cheaper goods from overseas. It is true that the kind of jobs people had in the past are largely gone. But this is nothing new. We moved from an agrarian society to an industrial society to an electronic society. In these changes, the economy must transform along with the culture. Very few Americans now work in factories. That’s good. It frees Americans up to work with emerging technologies.

If you have further questions about the sustainability of service economies, I suggest looking at what economists are saying. Don’t listen to pundits who sell fear. Listen to trained and educated professionals who earn their livings on analyzing economies. They agree that our economy is better for us in the long run (though there can be short run pains), and is sustainable.
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No it isn’t. Without manufacturing and the huge numbers of good jobs associated with manufacturing processes and supply/distribution you are left with an un-balanced economy that needs just as much income, or more, than your country needed before your country switched paths towards an all-service economy. Ensuring that your country’s un-balanced economic model succeeds becomes an all-consuming political necessity and that in and of itself encourages the introduction of unwise measures that become established economic policy.

At least I think that’s a plausible argument to consider.
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