1. Get lipo bag if you're concerned. I've had so many puffed batteries (some severe) but never had explosions (lucky I guess). You can continue to use it no problem based on your description.
2. Storage mode is always slow for most chargers. It doesn't go above 1A. If you plan to use the battery again next day, you don't need storage mode. But like Adamska said, if you overuse the battery, the voltage will be very low and then you will end up losing the battery w/o properly keeping the battery. Just check the voltage after usage. If it's too low, you'd better bring it up close to 7.4V. If it's higher than that and you will use it in a few days again, leave it alone. If you won't use it for more than a week, keep it at storage mode. Just leave it overnight.