Answering questions sounds fun. For reference though, I don't do a lot of worldbuilding based around civilizations and such. Or maybe I should say that when I do, I usually use an existing ones as a sort of template.  

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>First and foremost, how do you build a fictional economy and do you even need to?
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As with all things, it's only important if it's a part of the story. 

Making them is pretty simple though. If you have a medieval town located in the woods, something was there that caused a settlement to form. Maybe the wood is of good quality, or the nearby river has lots of beavers to skin for hats. So you have a lumber yard/skinning hut that exports its goods to bring wealth into the town. If there are enough people doing it, other people move in to provide services to the workers, such as the town doctor. Boom, basic economy. 

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>Second, do you need to create conlangs or can you just reference the fact that a character is speaking X language and leave it at that?
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If language barriers are not a part of your world, you don't need to address them. Otherwise, I usually say that someone is speaking in a foreign tongue. Sometimes I'll use brackets to make it apparent someone's not speaking the protag's language if I want the reader to know what's being said. But that is a stylistic choice and not the only solution. 

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>Third, is it possible to worldbuild a faction or civilization that has no culture? If so, what would that look like?
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What's your definition of no culture? The closest examples I can think of would be a melting pot where there are so many cultures they all sort of blend together, or a society without traditions and standards of any kind. Maybe very early cavemen didn't have culture? I would think that any group of people are going to form their own beliefs about how things should be done and a culture is going to come out of that. 

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>Fourth, if your factions are run by gods then do you even need to go into depth on anything but the deity in question? And by deity I mean the omnipotent, can do anything that it pleases, kind. Not the Greek or Roman kind.
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Yes, because followers of said deity seldom share the exact same mindset. Maybe if said god is a wicked creature that uses their subjects as an extension of their will, but even the Ossiarch Bonereapers in age of sigmar, skeletons that are an extention of Nagash's will, have their own history and culture apart from the necromancer that's brainwashed them all. 

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>Fifth, do you start fleshing out the world itself first, timeline of events, or both?
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I usually world build to add depth to a story I want to tell. So I usually figure out details about the world before working on the timeline that created that world. I think it depends on what interests you more.