2003 Ford Explorer Battery and Electrical problem

I have a 2003 ford explorer with 43,000 miles. Original battery.
The door ajar warning indicator comes on when all doors are shut. The doors don't lock automatically when put in drive. The security lights and overhead lights remain on longer than normal after locking doors. The key pad works to unlock the doors but not when you unlock doors. Lately, my battery has been dead, but, jumpable. Is the electrical problems draining my battery or does the battery need to be replaced? Is my electrical problem easily fixable. Thank you.