Let's say a citizen is able to launch a rocket or a weather balloon into space with an electronic device (probably a GPS) and a small gnome attached on it, would it be legal?
Does this require to notify government or a particular agency?
Technically these are unmanned (but not ungnomed) drones and the law about them is here.
If your craft in flight is less than 35kg you do not need permission, however, a craft that small is not going to get to 100km (the boundary of "space"). You therefore need permission ... and insurance in case it falls on anything or anyone breakable.