They should fit together, as the details on Newegg say it supports these form factors:
ATX, Micro-ATX "
Generally most ATX cases will also support Micro ATX boards.
As well, the cooler master website claims it supports Micro ATX boards:
"Elite 334 (NV-334) is a Nvidia Edition mid-tower that accommodates micro-ATX and ATX motherboards..."
Hope this helps!
P.S. I think most people would recommend getting something like an HAF 912 for that price range as it is popular and very good (also cooler master). As well, keep in mind to check the details on wherever you are buying and the manufacturer's website to check for compatibility as they will usually tell you!
According to the website, it comes with 2 standard 120mm fans, but can support significantly more.
If you are not overclocking much/in a cool environment you shouldn't need anything more than those standard.
Otherwise, maybe look at getting some more fans in accordance to this image from their website.