A good item to start on is the battery drain problem.
The whole electrical system should pull 50 ma or less of current with everything off. A 7-minute wait is necessary before testing so that timer circuits can time out and quit pulling current.
Is your meter digital or pointer type?
What is the highest DC current range on it?
What is the lowest DC voltage range on it?
Dream tool to have here is a clamp on DC ammeter.
Does the car have any aftermarket electrical equipment such as stereo, amp, lights etc?
We don't want to try measuring the current directly if it is more than the range of your meter. It may be pulling several amps at rest if it runs the battery down in a few hours.
One easy thing to eliminate is dirty battery connections. Make sure there are no signs of corrosion on battery terminals or cable connectors. Clean them anyway with a wire brush or similar tool.
What has been, can be again. (Bob Wills, 1942)