A:AnswerYes, you will need to use ABC01F as a BT transmitter and connect to your sound bar's AUX or RCA output port after you paired your Bluetooth headphone to ABC01F.
A:AnswerYes, if you have a AUX/3.5mm input on your amplifier, you can stream music from your Bluetooth enabled source such as a smartphone to your amplifier using ABC01F in receiving mode.
A:AnswerIf your car's USB port continue to provide power when the car is not running, then no, ABC01F will stay on and it will reconnect to your phone automatically. But if the port does not provide continuous power and ABC01F runs out of power, you will need to power it on manually but you won't need to pair it again as it will still reconnect automatically to your phone.
A:AnswerIf your SanDisk player has Bluetooth function and your receiver has an AUX input, then yes, you can use ABC01F in receiving mode to play music thru your receiver.
A:AnswerQuite an odd problem you have going on. I have to wonder if it has something to do with the bluetooth headphones you are using. If they are an older pair yes they should be backwards compatible. I have to wonder if that is causing the delay. If you are coming directly out of the television and not running through any other equipment you should have a good sync. I have not experienced any problems like that. You may have a problem with that particular unit. Now there is a difference between Optical cable vs RCA. You can buy a delay switch to sync perfectly. When younger I liked listening to the radio when Caywood called the bsketball games. You need one of those switches now because the radio signal hits quicker than the television. They must run television through a delay in accordance with FCC regulations now in today's world.