Running 5VDC circuits off a rechargable ni-cd batteries that can recharge in-circuit from a DC power supply
I would personally look for a battery management IC and modern battery technology that is not an environmental disaster (Cadmium)... But if you insist on doing NiCd, you have some things to watch out for:


NiCd batteries can explode if over charged. 
NiCd batteries suffer from memory effect, they should be fully discharged then fully recharged otherwise their capacity is greatly reduced.
Power dissipation in your regulation system, you will not be able to provide any large amount of power, nothing close to being able to charge a phone if that is what your plan is. Assuming even the lowest 500mA charge rate of a phone, your 5V regulator will be dissipating 1.5W. Move upto the 1.5A of a modern smart phone and your at 4.5W, even with a large heat-sink that will be hard to manage.


Continuing on, assuming a full open circuit charge of 1.3V, you should plan to charge the batteries to 7.8V or 8V as you suggested. Monitoring the charge will be challenging without some way to interrupt the charge and check what the floating voltage is. 

Also two items about your circuit, I did not spend much investigation but your variable voltage regulator seems overly complex with the addition of Q1 etc. Second, I would choose a low drop diode for D2, like a schottky, otherwise your 5V will look more like 4.3V and not power any USB based device (USB spec is 5V 5%).

Instead of redesigning the wheel with really old technology, you should look into how a modern Lipo based system works with a boost or buck converter. You could still build it yourself and it would be efficient enough to charge a smart phone.