What you call "aid from abroad" is generally called a functioning wide area synchronous grid (https://en.wikipedia.org/wiki/Wide_area_synchronous_grid) which covers most of the EU plus some Balkan states, Moldova, Ukraine, Turkey and the northwestern corner of Africa. So Germany can sell power to others when renewables are generating more than it needs (which is often), and import power, not necessarily because it couldn't produce it, but because importing it can be cheaper than e.g. starting up an additional backup plant. This is nothing special and has been working reliably for decades.
I call buying French nuclear electricity after shutting down your own reactors hypocrisy.
That's right, Germany sells electricity to other countries during the day and buys electricity in the evening because there is no sun then.
The problem is that other countries also have solar and wind power during the day and don't need this electricity at all. That's why Germany has to “sell” this surplus electricity, even though no one needs it. To ensure that the electricity is still "purchased", Germany has to pay money for it. In the evening, Germany has to pay money to buy back the missing electricity.
Paying money to have something purchased is generally referred to as garbage fees.