First of all, can not guarantee that your iPhone will work with that Handsfree Bluetooth, regardless of what any of it says. The iPhone is manufactured by Apple to work on its own, it is not made to work with any of these 3rd Party products, contact that manufacture for more information.
First thing I would try is on the iPhone go into your Settings > General > Reset > Reset All Settings
(NO YOU WILL NOT LOSE ANY DATA) Once you tap that, it will inform you that it will NOT erase any of your data, simply just resetting the settings, getting rid of any glitches. Test it out after this, if its still an issue, continue to the next step.
Best thing to do, since this mostly sounds like a software issue. Restore the iPhone using iTunes and a computer (Download iTunes here: www.apple.com/itunes ).
-Plug your iPhone into your computer using your USB Cable that you plug into the charger with.
-If possible, plug into the back of your computer if you're using a desktop.
-Open iTunes on your computer, make sure its fully update, a message will pop up telling you it needs to be updated.
-When iTunes is open on your computer, you should see your iPhone listed in the left-hand column beneath Devices
-Click on your iPhone, in the main window of iTunes you should see a Restore button half-way down the page, click that and it will ask you if you're sure.
-Agree to the terms, yes this step is going to erase all your data on your iPhone.
-iTunes does automatically create backups of your iPhone, however these can store corrupted files, and are not best used in a situation like this.
-For further information on BACKING UP your data by syncing, THEN restoring your iPhone, follow this Article: http://support.apple.com/kb/ht3828