1) inline amplifiers are tipically used in repeated systems (for example 1000km of 10x100km spans), they usually are required to have good NF, output power and mid-stage access in case of dispersion compensatio.
2) not sure I understand what post-amplifiers are…maybe you mean boosters?
3) preamplifiers are the last ones before the receiver section. These amplifiers need to have very good noise figure, while output power is usually low because their output goes directly (through demux) to the receivers. As Alitsu mentions, you can also use hybrid EDFA/Raman for preamplification of the optical signal.