Two Microphones 15 Hour Bluetooth Receiver /Bluetooth Car Kit, TaoTronics Bluetooth 4.1 Portable Wireless Audio Adapter 3.5mm Aux Stereo Output ( One Click Siri Activation,DSP/cVc 6.0/A2DP/AVRCP/AAC)

Download :

Sunvalleytek is committed to protecting your privacy. Learn More...

•TT-BR08 user manual

TT-BR08 User Manual.pdf  

FAQ

When connected, I think you could skip songs with the receiver's buttons. Hope this information helps.
Pairing should not be a problem, Bluetooth as a standard is backward compatible. That said, I do not have an iPhone with which to confirm this expectation.
Sounds like your aux cable and double ended connector is bad. I just had this same issue in my car. Only played music out my driver side speaker. Get a new cord or connector piece abs you should be fine since it doesn't do it with your headphones. Hope this helps you!
It automatically connects to your Bluetooth device but must be powered on and off manually.
Providing it has bluetooth, which most do , yes, I have done it with my Samsung 7
When connected, you could only use the mic of the receiver. But you could disconect the Bluetooth to use the wired mic of your headphones. Hope this information helps.
You would need an adapter cable. From the age of your system, I would guess you need a male 3.5mm stereo miniplug to dual RCA connectors (probably female). If your system is mono, you would need to merge the stereo channels into mono or playback just one of the two channels.