Remember to close your apps by spamming the back button until it stays on the home screen. It's a crappy way to manage apps but meh. Background apps do not get suspended in WP8 so they will drain the battery. Battery saver essentially does the same thing though.
This is NOT correct. Windows Phone DOES suspend apps. If an app is not in the foreground, it is not doing any processing. Background tasks are a separate process than suspended apps. Battery saver will disable the background tasks, though, but don't confuse background tasks with suspended tasks.
Suspended tasks are those which you see when you tap/hold the back button.
Background tasks, or Periodic tasks, which would be a better way to describe them, are run on a periodic basis in the background. The time between the periods that they run varies, but is based on when the phone is going to be turning the radio on due to tasks that the OS will be doing for its own purposes, because the act of powering up the radio is quite power-intensive, and Microsoft does this to conserve as much battery as possible.
Developers cannot predict with precision greater than a half an hour, and some recommend not planning for their tasks to run more frequently than every hour, and in fact you can't plan on it running at all, because as you can see from the threads, users can disable them completely, so you have to write the app so that it works without the background task at all - the background task in that case would be an enhancement.
This being said, this is how it works in Windows Phone 7.5 (Mango). I have not had time to dig into the Windows Phone 8 SDK, so I can't really say much about it, other than to say that I've heard word that developers can have a bit more control over when their background tasks run. I'm only using background tasks in one of my apps, and all I'm doing with it is checking to see if it is a new day, and if so, updating the live tile. The app I'm doing that in is a Weight Watchers points tracker, PlusPoints, and the tile shows the number of points that the user has left for the day, so at midnight I want it to reset to be their daily allowed number. My ratings are much higher than the official Weight Watchers app, BTW...
As for my battery, I've let the grandson sit here and play Angry Birds Star Wars for about two hours maybe, and that in addition to the other use I've had all day, which was probably a low day for me (though I do have quite a few live tiles), and that's left me at about 50%. For those who want to keep an eye on their battery use with better precision, here's an app for you:
Battery Level for WP8 And when you use it - keep in mind that the number on the tile comes from a background task - so it runs periodically - it is not instantaneous. So if you want up to the minute status, tap it.