The two extra diodes are likely to improve crossover from CC to CV mode and for protextion of the OP. It depends on the OP type of these diodes are needed or make sense. Usually the diodes should be anti - parallel, not in series.
The extra transistor helps a little to turn off the ouput stage a little faster. However this mainly makes sense if there is an additional diode / resitor from base to emitter at V3.
The part left out are for an analog meter - so not needed in the Version with digital display.
The current to provide the slghtly negative voltage, when current limit is set all the way to zero (or actually slighly negative) comes through R14. One way to fix this, could be adjusting the offset of the CC setting, so you can't set the current limit below about 1 mA. An alternative might be something to pull down the votlage at R14, if the ouput of OP4A is really high (e.g. > 2 V). However this might be a little tricky and should be simulated fist, as it could also effect (could be well be positive) the CC to CV transition and stability in CC mode.