When do the 0.5 BTC appear in Alices wallet?
It depends on the wallet software. Typically wallet software will show the BTC as appeared in her wallet as soon as the transaction is received by that wallet. It will be unconfirmed at that point, so it is potientially unsafe to spend the outputs in that transaction.
Does she now posses the Output of transaction A? Because this is an unspent output. Only when she wants to pay her employee, she unlocks this output, such that the input of transaction B consumes the output of transaction A. Then, her empoyee "holds" the output of transaction B.
Is this the correct way? In my understanding, an input only consumes a previous output, when someone wants to make a subsequent transaction. This is why this picture irritates me a little, because it says "Alice receives"... But isn't she already the owner of the output, before the input of transaction B consumes the output of transaction A?
So, in my optionen: Alice won't unlock the 0.5 BTC in order to possess them, but in order to spend them.
Yes, that is correct. Alice does not have to do anything in order to receive the Bitcoin. Once Bob has created an unspent output that Alice can spend, she can say that she has received the Bitcoin.
Of course, there is a caveat to this. Bob can't just make any output script that he wants that Alice can spend. There are a lot of output scripts that Alice could theoretically unlock and spent as an input in another transaction. However Alice is not tracking all of those things. Rather she has a specific set of output scripts that she can spend and she gives out addresses that correspond to those scripts. In order for Alice to consider Bob to have paid her, he needs to make an output with a script that corresponds to the address Alice gave him, otherwise Alice will not consider that transaction to be hers.
