In theory, it shouldn't matter how you charge it. It was recently shown that the latest batteries do actually suffer from battery 'memory' but the affect is apparently too small to notice.
Have to admit that I prefer not to do partial charges (i.e. not all the way to 100%) and I do occassionally allow it to run all the way down (until it turns itself off - the old way of addressing battery memory), but there's no proof this has any effect at all.
If your battery has suddenly started playing up, try removing any apps (or updates to apps) that you've recently installed in case they're doing something dodgy. Next, you could check the sync'ing options on all the apps you have that sync (e.g. email, facebook, twitter, news, weather, trains etc etc).
If none of that helps, it could be that there's an issue with the battery .. that would explain the sudden drops in charge and might also explain the black outs. I assume that you'd need to send the phone to google/LG to have the battery replaced.