I have a Sony DSC HX100V camera, but its charger is not working. Should I use a duplicate battery charger to charge it or not?
The general answer is yes, but there's a caveat.
There are a lot of cheap knockoff chargers sold in the global markets. Studies in the phone and laptop markets show the dangers, where occasionally something catches on fire and injures someone, and in almost all cases is tracked back to some really cheap charger. The same is true with cameras.
A lot of these chargers are very poorly designed and manufactured poorly. Some of them are dangerous and will invariably fail on you, perhaps destructively. So you have to choose a bit carefully.
My recommendation to people is to stick to fairly well-known manufacturers where there's some track record on their design and manufacturing quality. Companies like Transcend (which I use for some of my chargers) are worth looking at and are a good value compared to the official charger.
One way to judge is price. If it's really cheap compared to the official one, be wary. If the official charger is $60US, and the replacement is $5, stop and ask yourself what corners they cut to be able to make money at that price. You probably don't want to know the answer, and you don't want it anywhere near you or the equipment you care about.
(for more on the cheap charger problem, look at this: http://www.dailymail.co.uk/news/article-2406185/Fake-Apple-Cheap-phone-chargers-burn-house.html)
I do agree with chuqui about the dangers of aftermarket batteries and the validity of his/her comments but I do have an issue paying substantially more for a brand name product because it has "Sony" slapped on the side of it.
What I would recommend doing (and what I do) is finding a reputable 3rd party manufacturer. I would recommend you looking into a company named "Wasabi" or "Smatree". Both are fairly reputable and offer good 3rd party battery and charger replacements for a lot less than the name brand. I have 10 batteries between my 6 cameras that are made by Wasabi (gopro, 4xcanon, and fuji). All 10 batteries work flawlessly ranging from 6 months to 2 years old. You can validate what I am saying by searching on Amazon.com for Wasabi+"your camera name" and I've got a good feeling you will find a replacement battery and charger for half the cost of the name brand with great reviews.