If you add more weight on it to make it close to neutral buoyancy , you can make it dive as deep as you want. However, because of increasing pressure as your sub goes deeper, its volume will decrease, making it more & more negatively buoyant, resulting in staying at the bottom.
Usually the batteries do not choose to weaken & die together, & if one of the batteries in the pack dies earlier, your whole pack will not hold electricity as good. Replacing the weak battery link is a good idea & will help.
Extending or re-locating the antenna sometimes help but interference is inevitable due to closeness of components low power of RC system.