What is that?
 

http://images.cars.com/supersized/DM...7/83554.32.jpg
alarm system ? Trinket I mean... never seen///

Yup! It's the remote for an alarm system. Who's car keys are those?

Its from 4.8is saw it on ebay

Possibly remote start too - I have a separate remote for my starter.

they look like keys, alarm remotes on a owners manual...

Notice that the valet and wallet keys are missing...

there is an AUX button that can be programmed for different functions like auto start

so, this is native BMW alarm system ? from what model years X5 start to be equipped such system ?

no it is not the native alarm. The OEM system is engaged/disengaged by the key fob from BMW. Someone put an after-market system or remote starter on the car.

How do you bypass BMW Antiteft security to start with remote ?
Right coded key has to be pressent in the car in order for the fuel pump and electric system will work ? or does this apply for EU cars only ?

Much like any car that requires chip authentication (and almost ALL do now) you usually have a secondary key or chip fob that is part of the circuitry. When I use to install these systems it actually required a physical key. Systems now may be better.