Hi keyster,
I have had a turtle for years when I was a kid. Not sure which exact species it was, but it's a turtle. 
The water level I had was slightly higher than the turtle itself. So the turtle is completely submerged. Very often my turtle would keep its head above the water to breath the air. I'd imagine that would be harder to do if the water was deeper.
How big is your aquarium?
To think about it now, I believe it is a better idea to use the substrate to create a natural lake like landscape in the aquarium. So the turtle has the choice to stay in the water or come to the "shore". Of course, you need a pretty big aquarium for that.
Do you have a filter?
I did not have a filter for my turtle when I was a kid. But these days I have learned it is wrong not to have a filter. Most live organisms produce ammonia, and it is toxic. You need to pick a filter and have it run 24/7 to keep ammonia at 0ppm. You can see the article here,
http://petskeepersguide.com/choose-an-aquarium-filter/
As for eggs, don't worry about it since your turtle can't reproduce without a male friend. 
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