Yes, Comio C2 does have the memory card slot.
No. Comio C2 does not have the fast charging support but you can use Sony CP-AD2 USB Charger to charge it faster. By using Sony CP-AD2 you can reduce the charging time by almost 35%.
Comio C2 comes with big 4000 mAh battery. It offers talk time of up to 20 hours and standby period of about 500 hours.
It takes about 4 hours to fully charge the Comio C2. That is because it has huge 4000 mAh battery. If you use any good quality fast charger - the charging time can reduce by almost 35%.