parting and parallel woes

[misterroy]

Hi, two of the lathes at work don't do true parallel cuts, they get narrower towards the headstock. Is it likely to be fixable by moving the tailstock sideways, or is it more likely to be the bearing at the headstock end?

They all have problems with snapping parting tools, too much play in the cross-slide?
Can the bearings be tightened?
Buy a new nut for the feed?

thanks