If I could somehow store a plane inside another plane, would I be allowed to start the second plane somewhere in the air? Maybe different countries have different laws for this kind of aviation?
I know that this is technically at least challenging if not impossible, I was just wondering if I would even be allowed to do this.
Bonus Question: How would the pilot communicate this to the authorities?
At least in the US, this is perfectly legal. There have been quite a few such aircraft in history.
However, an aircraft docking and undocking from another is so rare that there's no standard way of communicating it with ATC. So you'd have to explain what you're doing in plain language. (And then you'd have to explain it again when the confused controller replies, "What?") If I were flying such a mission, I'd contact the local FSDO ahead of time to explain it, so that they can forward the information on to the local ATC facility to cut down on confusion.
It is possible- which is a strategy that is commonly thought of in conjunction with space tourism. You can not only start a plane in air using another airplane but also start a hybrid rocket from an airplane in air. For that look up SpaceShipOne and its carrier aircraft.
