I know plants take hydrogen from water. What happens to the hydrogen when the sugar or fat it was turned into either burns or breaks down and decays? Does it go back into water somehow?
Yes. That is what burning does. It attaches oxygen to the hydrogen atoms.
Water is the ash of a hydrogen fire.
ETA: ninja’d, but I got a couple extra points in, so you’re stuck reading it. 
When a carbohydrate burns the carbon & hydrogen become separated and combine with oxygen from the atmosphere. The resulting exhaust is CO2 & H2O. IOW carbon dioxide and water.
A real reaction has a few other things going on than that simplified version. But it’s close. The metabolic process by which, say, an animal cell, converts plant carbohydrates into energy to live isn’t the same as simple burning. There’s lots and lots of side trips, enzymes, and other funky stuff going on.
But chemistry wins in the end. Just like rocks roll downhill, not up, once molecules get rattled around enough they reform in the direction that releases energy, leaving the new molecules lower in inherent energy. Carbohydrates “roll downhill” to (mostly) CO2 and H2O.
In a pretty high level “meta” sense, Life writ large is simply a mechanism to temporarily and locally drive chemistry in energetic reverse, winding up a chemical “spring” for use later. When we run the spring back down we get energy out to use for whatever.
Part of the problem with doing something useful with CO2 exhaust to combat global warming is that CO2 is pretty much the ultimate “ash” of a chemical process. It’s what’s left after you’ve wrung almost all the energy possible out of the earlier stuff. So anything useful we try to do with that ash chemically will necessarily involve injecting a lot of energy back into it. And since right now most of our energy comes from burning fossil fuels, that’d end up with us chasing our tails.
When it burns with enough oxygen, it does turn into water. A very small quantity is present in tar as phenols or other compounds - depends on how well the combustion happens.
If burnt with less oxygen (gasification) it turns into Hydrogen / methane mixture with predominant hydrogen.
Again for break down and decay, it depends. It can turn mostly into water (coal), heavy hydrocarbons (oil) and methane ( natural gas ). A very small part of it also forms Compounds like Hydrogen sulfide and ammonia. For coal, the older the coal (anthracite), the less Hydrogen it contains while newer coals like lignite has plenty of hydrogen compounds.
!
Props.
“I’ve fallen into burnt hydrogen and I can’t swim!”
Dennis
The production of “metabolic water” from carbohydrates is the reason that some desert animals such as kangaroo rats do not need to drink liquid water.
Only if the hydrogen fire is with oxygen. You can have Hydrogen fires with halogens like fluorine and chlorine.
To add on to my previous post, ethyl alcohol is a common way for hydrogen atoms to end up when carbohydrates are metabolized in anaerobic conditions.
In other news
1000’s of people were killed today when a deadly mountain of hydrogen ash came out of the indian ocean and swept many miles inland.
You know, if somebody bottled water and called it “metabolic water” they’d probably have a winner.
I doubt it. Most people would assume it meant urine or maybe sweat.
Yeah, I guess so. 
ETA: Pocari Sweat,which I used to drink back when that was its only (English) name. It’s tasty.
And of course, you can substitute “hydrocarbon” for “carbohydrate” and the exact same thing is true. Hence the CO2 and H2O (and many other byproducts) from burning hydrocarbon fuels. The liquid sometimes seen dripping from your car’s tailpipe is condensed water (usually when the engine is cold, before it’s hot enough for the water to emerge as vapor). It’s also a contributor to aircraft contrails that emerge behind the engines, although that one is more complicated and a lot of it is often atmospheric condensation around the aerosol particulates in the engine exhaust, but water from fuel combustion is part of it. Contrails are essentially high-altitude ice clouds and, perhaps surprisingly, in conditions where they are persistent they produce (on average) a small positive climate forcing.
Run away!!! Run away!!