Camera sensors have an specific number of cells,and their resolution depends on this amount of cells. But film does not have this "units" of sensible material; So, does the size of the particles of the film's light reacting coatings determine its resolution, or can it be said that film has an infinite resolution?
No, you cannot say it has infinite resolution, despite what CSI may have people believe :)
A film particle puts limits on how fine details can be resolved. It gets complicated though because film has grains of different sizes. Every frame is composed of grains of different sises and they are intermixed. Larger particles are more sensitive to light and used to render details in shadow areas while smaller grains are for keeping details in highlights. Film would not really work if all grains would be the same size.
The size of light reactive particles (grains) certainly is a major factor in a film's resolution, and it definitely can be said that film does not have infinite resolution.
The resolution of film and digital sensors is generally specified in the same way, by it's modular transfer function. And the photo-site count of a sensor (i.e. number of pixels) just serves as an approximation of it's actual resolution.
On most digital cameras, if one cranks the ISO up to maximum, one will nominally have the same resolution as at a lower ISO setting, but the picture will have a lot more noise (parts of the picture which appear lighter or darker than they should). Such noise will make it harder, or in some cases impossible, to observe all of the fine details in a picture. The only digital cameras which do not have this behavior are those which restrict the range of ISO settings below the point where noise would become a problem.
Film can generally be thought of as having no hard resolution limit beyond the fact that it has a certain amount of noise; the more one magnifies the image on the film, the more apparent this noise will become, to the point that it may dominate everything else. Much as reducing the ISO setting of a digital camera can reduce noise, likewise with selecting a lower ISO film. If one has a certain amount of tolerance for noise, one can for a given kind of film and set of exposure conditions, define the maximum resolution where the noise would remain tolerable. The more noise one can tolerate, the higher the "usable" resolution.
There are, of course, some hard physical limits to the resolution of film, but most film is not used anywhere near those limits. Further, because film--unlike digital camera sensors--contains a somewhat random arrangement of light-sensitive molecules, it does not exhibit the aliasing problems that can sometimes digital cameras. If a digital camera is focused on a wall which is placed at a distance so that each pixel represents one inch, and the wall is painted with alternating 0.8" black and white stripes, the picture may (given perfect focus and perfect optics) show alternating four-pixel wide stripes of 60% gray and 40% gray. Such phenomena are not a factor when using film, since it lacks the regular arrangement of light-sensing molecules. If a film camera were to take a picture of such a wall, any particular part of the film showing a white stripe would have a higher probability of being dark (assuming negative film) than the areas exposed to dark stripe.