First is when the outside temperatureis between -10 and 0 degrees celsius my rear axle sometimes locks up. It only happens when I slowly make a tight turn like parking in a mall. It will lock up and then after one of the tires slips then it's not locked up any more. Has any one had this problem before?
The second is my door lock is frozen. The lock cylinder is fine I can only open the drivers side from the inside. When I lift the interior handle the lock pin on top of the door lifts half way up. This lets me open the door. When the interior handle returns to the down position the pin goes down with it and the door is locked again. I don't have a garage to warm it up in and the outside temp won't be going above freezing for a long time. I've white greased the cylinder and the latch parts and it didn't help. Any suggestions?
I have a 2004 4x4 Laramie edition.

 

Its a 2004 Ram 1500.

 

Let me guess, Did you have your truck in 4x4 before this happened. ? If so ,drive it down the road in 4x4 then stop then put it in 2x4 then back up about 30 ft.Then go forward a while Then try the turn thing and see if it still happens. .If you don't do this sometimes the truck is still in 4x4 almost. It's hard to explain but the gears haven't locked properly.

 

How many miles on your truck? If you haven't changed the gear lube in the diff's, it may be past time. If you have had them changed, its possible the friction modifier that's required for your rear diff is starting to break down or there possibly wasn't enough added. All the 9.25 light corporate axles require the friction modifier for the clutches to work properly, and when its really cold outside, the gear lube is substantially thicker even if it is synthetic, assuming that you have the original OEM lube in there (mopar).
The service manual asks for rear and front diff to be changed every 15K miles (24k-kilos). Due to the temps you have up there, you should follow the Shedule "B" in the from the owners manual
Hope this helps