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1) Are uncoated lenses more prone to haze problems?

In general, yes. In particular, it depends on the number of lens
elements and on the skills of the lens designer to avoid internal
reflections, i.e. using cemented surfaces instead of glass-to-air
surfaces. However, I am not the only one who made (technically)
excellent shots with uncoated lenses. Use a lens hood if possible and
avoid shooting against the light.

2) Would using B&W film eliminate this problem?

No. B/w film will register the reflections/haze in the same way as
color film. Some people claim that uncoated lenses are suitable for
b/w only which is quite far from the truth.

3) Believe it or not the camera has provision for behind the lens
filters. Would behind the lens filters perform better than placing them
up front, and consider that these are uncoated lenses?

Probably not. A reflection is a reflection is a reflection, whereever
it occurs. It does not matter whether the reflections bounce back and
forth between the front lens surface and the rear surface of the
filter (when mounted in front of the lens) or between the front
surface of the filter and the rear surface of the lens.

Winfried