Charging appliances with chargers of different amperage (safety & duration)
A properly designed charger will not take any damage (apart from maybe a blown fuse) if the load is too high. That of course does not apply to 2$ charges from China..

The current rating of a device usually is the maximum current it consumes, given the specified input voltage (range). So no, using a 2.1A charger on 1A device shouldn't change the charging speed.

This applies in the general case, where a "charger" simply is a constant voltage source. There are some exceptions to this though, so be careful, unless you know what you're doing.