Underground filter quiz?

We purchased a small fish tank (1 gal) for our daughter, it came with an underground filter and I'm merely wondering can I put the water level higher than where on earth the water comes out of the filter? Just because it doesn't go all the course to the top of the aquarium and also because its leaving air bubbles at the top of the tank. We enjoy a betta and its affecting him being able to get to his food.
I haven't have much experience with filters.
Tell me what you deduce just about...
Answers:    It really isn't necessary to run a filter for a betta. They enjoy lungs and come to the top to get air. They will be a little more busy in warmer water but lately plain room temperature is okay with them. I would not leave a bedside light on all the time as it will change the temperature. One gallon of wet changes quickly. Natural light is freshly fine.
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