I would like to know if a WMS exists for Sentinel 2 images?
If yes, its use is it free?
And is it possible to make a calculation on the fly, like NDVI?
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You can check out Sinergise Sentinel Hub as well as the Sentinel Playground and Sentinel EO Browser. There are a mix of paid and free WMS, as well as on-the-fly remote sensing claculations, including several pre-existing spectral indices like NDVI.
Disclosure - I do not work for Sinergise but rely on their products which I find useful.
I'm not aware of a Sentinel WMS as one of the main benefits is that users can select scenes they want which would be difficult to implement (in my mind at least).
But there are a number of viewers and this is the best one that I have found so far.
It lets you preview data in various band configuration and has NDVI and other indices already calculated and viewable. It even lets you do split scene viewing to compare scenes taken at different times over the same area. It does have a daily scene limit which requires payment to increase but I think it would be useful to you.