Question

1. Can we receive any notification from a bluetooth device, even if our app is in background?
2. Is it possible to launch an iphone app by sending some commands from a bluetooth device?
3. Is it possible to wake an app which is running in the background in similar way?

UPDATED

Apple says this in App States and Multitasking part of iOS App Programming Guide

Communicating with an External Accessory

Apps that work with external accessories can ask to be woken up if the
accessory delivers an update when the app is suspended. This support
is important for some types of accessories that deliver data at
regular intervals, such as heart-rate monitors. When an app includes
the UIBackgroundModes key with the external-accessory value in its
Info.plist file, the external accessory framework keeps open any
active sessions for the corresponding accessories. (In iOS 4 and
earlier, these sessions are closed automatically when the app is
suspended.) In addition, new data arriving from the accessory causes
the system to wake up the app to process that data. The system also
wakes up the app to process accessory connection and disconnection
notifications.

What does it means?
Can we use remote control events to achieve what i asked above ie Waking up an app from background. or is there any other way to do this ?

Answer 1

1. No this is not possible
2. No this is not possible
3. No this is not possible

Unless you jailbreak the device.

UPDATE after EDIT:
No this is not possible.

As was pointed out in the comments, this is straying towards the MFi territory. I suggest you search around the documentation a bit more.