1. Capacitor value does not necessarily depend on the type of rectify used but rather to the load and the frequency of the ripple or the AC used to rectify
2. A full wave bridge converts both the +ve and -ve half cycle of the AC Voltage to a usable DC value. That is why it is referred as a full wave, on ther other hand a half wave discards one half of the AC cycle.
Got it.
There is a good overview on wikipedia of the bridge rectifier and the reservoir capacitor.
A bridge rectifier is a full wave rectifier. A full wave rectifier can also be built to use a center tap transformer which is not required in the bridge rectifier.