Peugeot 307 electrical problems

Hi all, first post here, the guy who helps me with mechanics is usually good but is stumped here (he's checked computer, no errors showing,and suggested a new battery might sort it, which i forked out for and it hasnt)
The problems are all electrical which began with:
1: the car has mirrors which close in when its locked, and open when the igniotion is turned on, the drivers side one is very finikety, more often than not it doesnt open, and i have to lock and unlock with the remote,then turn the key in ignition just to the point where the starter would engage, before the mirror opens.
2:the drivers door window often winds down when i press the up switch, and goes right to the bottom before it will wind back up.
3: about 2 weeks or so after the new battery was fitted, the same problems this was supposed to cure returned, those being - when getting in the car first of all the center display reads 'ecomony mode' im aware that this means the battery is low so not all the electrics will work, although the car does start and the message then disappears but once moving the center display then keeps flashing an immage of a car (like the door open image but with the bonnet area lit up rather than an open door) once that begins happening the alarm goes off within a few minutes of locking the car.
OK, thats a lot to say on a first post, im hoping somebody here with considerably more knowledge/experience thyan me can point me in the right direction though (nice guy, and generally good as my mechanic is, it seems electrical issues arent his strong point though) many thanks in advance!