Can I connect iPhone and bluetooth 2.1 device and work with them via Core Bluetooth? I just need to send and receive some NSString data from/to iPhone.
No, Core Bluetooth only supports Bluetooth Low Energy/Bluetooth 4.0 devices. You can only connect to Bluetooth 2.1 devices via the MFI program and the external accessory framework.
The only exception is "standard" devices such as keyboards and audio devices (hands free etc). However in these cases you can't access any underlying Bluetooth information - you can simply send audio or receive keyboard input.