Last week, I opened the boot to get my bag out and unlocked using the button on the remote. When I tried to lock it, it wouldnt lock. I didnt think much of it at the time, thinking the battery might have died but I found it odd that the car didnt warn me like it did last time ("battery low") message ...

Your heater core heats the air moving through it (from the blower) using hot coolant from the engine block. its only after a few minutes of running that the block heats up enough to heat up the coolant and thereby the heater core. this is perfectly normal