Is the couple 解ける / 溶ける related to the English solve/ dissolve? I've noticed that which means 'to be solved' and , 'to dissolve' are pronounced the same way. Furthermore the second one can be written using the kanji of the first one. That relation between both words is really similar to the one between the English word solve / dissolve, which made me ask that question: was the use of the words / influenced by the English language? (e.g. solve a mystery as a metaphor coming from dissolving a chemical)

I think the pair was probably not influenced by the English language.

Rather, it is more likely a standard example of the very common phenomenon of a (native Japanese) verb being written with different _kanji_ to differentiate between various nuances/meanings. There are many, many such verbs

> → "to see", "to watch", "to look after", "to examine"
>
> → "to hear", "to listen", "to have an effect", "to function"

(Monolingual dictionaries will list these as "same origin".)

Of course you're correct in observing that this phenomenon is similar to the one of a verb like _solve_ taking (in this case) a prefix to convey a more nuanced meaning, such as _dissolve_ , _resolve_ , _absolve_. But of course, correlation does not imply causation.