There are two major types of headset- older, threaded headsets that have a quill that drops into the stem of the fork creating an interference connection, and newer threadless headsets that the stem is bolted and clamped on to. Flat handle bars are preferred by off road cyclists who can ride in a more upright postion whilst still having the controls at their fingertips, whereas drop handlebars offer more cycling positions and are favoured by road cyclists who typically spend more time in the saddle. The controls attached to the different styles of bar are operated and maintained in different ways.
Modern bottom brackets use a sealed bearing type construction that keeps water and debris locked out, so they seldom go wrong. Maintenance is impossible so they need replacing when they do wear out. Older style cup bottom brackets need to be re-greased every now and again, and occasionally will need to have their bearings replaced. There are a lot more teeth on the chainring cogs than those on the rear cassette, so need changing less regularly. Cranks usually a solid one piece construction so there is not much to go wrong.