Yes, Comio C2 does have the beautfy mode.
No. Comio C2 has a dedicated MicroSD card slot. You can use 2 sim cards and 1 memory card at the same time.
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 has micro size slot for sim cards.