聞こえる is it's own verb for when a sound is audible.
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聞ける is the potential form for other potential uses of 聞く, usually 'can ask' but also sometimes for 'can hear' in the sense of ability.
見える is again its own verb used for all the potentials of "can see".
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見られる is the passive and potential of 見る. It's used for all passive cases, but can be used for the potential in some cases,
mostly in the sense of having sight.
~ことができる is when used with 見る・聞く is mostly for a meaning like "has the ability to", but fundamentally the phrase
just means "(subj) can ~" and any verb phrase can be made into a potential with this grammar, and then used in many ways.