DIY Bluetooth speaker - Some power related questions
1: Not entirely by the looks of it
2: 12V 2A adapter typically, but do check the manual of the specific TP5100 module you have, as there must be many different ones made and sold.
3: No, for many reasons. First is that you get only standard 5V out unless you make something that fakes to be a quickcharge module to get 12V out. Even if you manage to do that, it can only output 1A at 12V and it can't give 2A to the charger.
4: Not sure what would you plan to use the relay for.
5: Add some circuitry to change the components to be supplied from charging port, but then the power supply must provide charging current plus the component operating current.