'matfrost' is right, if its a 2nd Gen MINI (Sept 06 > ) then you will be able to programme the locking feature yourself, as well as things like 'follow me home' lights where your headlights can stay on for a set amout of time after locking the car, or how many flashes the indicator does (1 or 3). If its a 1st Gen (01 > 06) then a dealer would need to do it as they plug it into their computer and reset it that way, they will probably try and charge you for it though, unless you know how to sweet talk them into it for free, or they are feeling generous (it takes no time at all to do it, I know I had it done on my ONE

) I also had the first one set to unlock just the drivers door when I pressed the remote, then when I pressed it again it opened the passenger door.
As for the window being open and the alarm, something would have to trigger the sensor inside the car (on the roof) and that will set it off. Everytime ive had a new car ive purposely set mine off to make sure it works, and I do it by sticking my arm in

It als works on movement/tilt sensor as well, thats why being on a ferry will often set it off
One touch up passenger window? My new Cooper S (June 08) has it as standard

however the earlier cars dont, neither do 1st gen MINIs. You can buy the wiring to do it on 1st gen though from Mikey --->
NewMINIStuff.com