being how they are li-ion cells, i would imagine the NTC thermistors would be to monitor the temperature, going to a comparitor with a significant hysteresis so that it resets and tries to continue but only once the cell has cooled back down, say tied to the enable pin of the charge controller,
to keep the costs down i would probably chase 10 seperate charge controller chips, as single cell cargers are far cheaper than dual cell ones, also helps for seperate temperature regulation
as for using an ATX PC Power supply, yes your generic unit should be capable of 10A at 5V, but have a look on the label on the side, and whatever value it says for 5V times it by 0.7, as you want overhead and sometimes 5V ratings can be a little fudged, e.g peak rating, to hotwire "most" ATX supplies, on the 20/24 pin big plug, use a paperclip or a piece of wire to bridge between the green wire and any black, that should get it capable of running in a way you can test it with,
other suggestion would probably be to use a 13A fuse on your 5V tie in, (keep you from hurting the supply) and a 1.5A per charge controller (stop you from hurting a chip or cell), as playing with a hotwired supply carries the significant risk of a short,
also when running of a atx supply of unknown origin, make sure your charge controller can handle 6.5V max, though very very rare i have seen ramp up peaks that high in some supplies,
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