Haze, uncoated lenses and B&W film.

I've been working with a camera in my collection that's got a whole
bunch of neat features. I noticed excessive film grain with the first
few test rolls. I then tried two other films and saw exactly the same
effect. This is color E6 film and the lenses are uncoated (pre-WWII)
and I haven't been using UV or haze filters. Now I'm thinking that what
I thought was grain is actually haze. But this haze is more extreme
that what I've seen with coated lenses. So here are my questions:

1) Are uncoated lenses more prone to haze problems?
2) Would using B&W film eliminate this problem? (I assume it would as
this is a high-end camera and I don't think the photogs of yesteryear
would have put up with this)
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?
Thanks for any answers or even informed speculation.