A crossover filters an audio signal by frequency. A simple way to look at it is, a crossover is what keeps tweeters playing high frequencies, mids playing mid frequencies, and subwoofers playing low frequencies. Most modern amps and some head units have built in crossovers, and component sets include passive crossovers. Crossovers are must have items but for most people the crossovers in their amps and the passive crossovers with their comps will be enough.
An equalizer adjusts the level of the signal in certain frequency ranges. The bass/mid/treble control on a head unit is a 3 band equalizer. The more bands the more you are able to tailor the sound to your liking. If you aren't competing in SQ competitions or a serious audiophile you probably don't need a 30 band 6 channel EQ, but all systems can benefit from some form of EQ.
A preamp is used to boost the signal between the head unit and amplifiers, think line-driver, most EQs include a preamp these days.
The Epicenter is a bass restoration processor, it uses harmonics to add bass where there was little to no bass in the original recording. When the Epicenter was released in the 90s my buddy's shop used to demo it with Van Halen 1984, it made a big difference, but not every recording needs bass restoration. The Epicenter is a cool toy but definitely not a must have item.