'How to' books usually don't have question marks at the end of the title. On the other hand it is common to say things like: "how to put this gently?", "how to do this without screwing it up?", "how to make her understand?". If a person says that then they are obviously interested in it themselves, but they could equally well say "how can I put this gently?", "how can I do this without screwing it up?". So maybe they are interested in the solution but not determined it has to be them to execute it.
I suspect "how to explain it to you?" is a good translation.
Not really. What you have to remember is that "to you" is expressed with dative. объяснить can take both accusative and/or dative: As a matter of fact, in this exercise, это is accusative, because it's the direct object of объяснить while тебе is the indirect object.
объяснить тебе слово - to explain the word to you
объяснить тебе женщину - to explain the woman to you [but I'm not sure if Russian uses объяснить to explain people].
It seems «мне можно» is omitted in this sentence. I learned in the previous lessons that «нужно» can be omitted in questions, only when using «мне» and «нам». Then I assumed «можно» also can be omitted in the same way. But I did not know the sentence where both «мне» and «можно» disappeared all together. What kind of situations does this happen in?
"Можно" is not good in such a phrase, rather you can say "Как я могу тебе объяснить это?" or "Как это возможно тебе объяснить?", but both variants sound a little bit odd too. I don't know whether any exact rule about omitting in such constructions exists, but it seems to me, when you see "can I" and the meaning is not about only me, but general - in this case you can omit it.
Japanese is exactly very different from any European languages, but it seems that there are no small grammatical similarities between Japanese and Russian. I have hardly felt such similarity between Japanese and English. If you are a native Russian speaker, I bet you will feel something familiar to Japanese ;)