Would all of the guardians perish? Keeping in mind that if the Traveler does indeed "die", it's protection would be gone and everyone would be vulnerable.
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I was under the impression that it had already died while keeping humanity from being wiped out and that the only part of it still functioning was whatever technology it used to maintain flight. You have to wonder who the heck thought that building a city underneath of something that massive, when they weren't even sure how it worked, was a good idea.
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If it dies, it would crush the city.
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Humanity would be screwed. Let's just leave it at that.
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I'm sure we will find out eventually.
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As the city is built within the shields of the traveller it could make things awkward.
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I don't think the Guardians are kept alive by the Traveler's power (in most cases). But I could see it affecting the Awoken or maybe even the Exo somehow.