The common allotropes of carbon are amorphous (no shape) graphite and diamond. Fullerene is, as you say, quite uncommon. The commonest one is amorphous - it's what coal, etc, is made from.
IAC, the carbon in carbon fibre is just that, fibre. It is formed (almost certainly from amorphous carbon) into fibres and used (as you say) with some form of resin, like glass fibre, to make objects. IOW, just the same way as cotton, asbestos and other materials are formed into friction blocks. It has to be at least reasonable as a frictional material (better than greased leather cone clutches, as found in, for example, Morgans) the only question you are likely to have is about its value for money.