There's mountain biking and mountain biking. Cross country on reasonable tracks is quite reasonable to undertake without a helmet, technical stuff where you are entirely likely to fall off, or stuff with lots of low hanging tree cover where you'll bash your head against branches, makes more sense to have one on. Downhill work without one (but the sort of full-face thing the BMX folks are wearing in the Olympics, not an EN1078 standard helmet) is kinda mad, but OTOH it's kinda mad period from where I'm standing...
Like footwear, fit is paramount. If a lid doesn't fit reasonably well it won't afford you the specified protection. The padding and adjustable cradle will take up some slack but the basic right shape is fundamental, and you get that by trying on in person, just like boots.
For old helmets, note the general advice that they should be replaced every 4 years or so if they've lived a quiet life. If they've taken a hit, straight in the bin.
Pete.