Not only in Germany, as per Commission Regulation EU 2016/631 systems under 800W are not regulated as power generating facilities - you just need a two-way meter installed on request by your power company and you're good to go.
Yes - such devices need a constant grid output to sync to. When the grid drops, their output drops. Furthermore, at 800W, it wouldn't be able to put any voltage onto the grid even if it tried to as it would get overloaded (it'll be trying to power up the entire neighborhood).