That seems to be the case however I never tried the 5w charger that came with the mini to compare it. I've heard 5 hours for full charge on the 5w but have not confirmed that.
As for it damaging the battery, Apple says its compatible with the mini so I picked one up. It's faster than my 10w charger but by how much I'm not sure.
Posted this last night:
Here is my unscientific results. I connected to my 12w charger when my battery was at 14%. It took 2 hours and 22 mins to get to 100% charge.
14% at 9:53 pm
59% at 10:53 pm
95% at 11:53 pm
100% at 12:15 am