If I recall correctly, the price in daily discount does increase, for that day. For example you buy the SS for 10 points, next will be 20 and so on. But after the day past, it is reset to default price of original discount.
I didn't notice there were different chest, no wonder sometimes I get more things sometimes less XD
Pvp is against people around your level, so get the Belly chain necklace on your pet and utilise it to kill your opponent.
On the other hand, +1 stat pill can use on my human pet?