They only accept typos if it's not a word (the = te accepted, he not)
It is grammatically and lexically correct also to translate 'kannst' with could, so the answer 'could you show me the way' should not return as a wrong answer, as it currently does. Grammatically, all three (would, can (of which could is really simply the 'hypothetical' or past tense)) are grammatically correct, with 'would' and 'could' simply being more 'polite' than 'can'.
That is wrong and you should not be spreading around this information. Each of those words means something different and has its own translatable counterpart in German, each with its own conjugations:
would = würden : Würdest du mir den Weg zeigen? could = könnten : Könntest du mir den Weg zeigen? can = können : Kannst du mir den Weg zeigen?
While you sometimes might be able to interchange them without someone caring about the difference, they are not just more or less polite forms of one another. That is why your answer was marked wrong, as they are different words.
Sure, but in the case of this particular sentence me being in the dative case is less a result of zeigen than it is a result of sentence structure. You could exchange zeigen for weisen and me would still be in the dative case, but weisen does not force a case in the way zeigen or geben does. So no, you are wrong. Zeigen requires the dative case, but here it is a result of sentence structure, and not that particular verb. So you're right, but not for the right reasons ;-)
I translated Weg as a method. Is it ok ? Little green thing does not accept my answer.
"der Weg zeigen" is simply show where to go, without losing time and energy to explain, considering the hurry people already have in the street. That's why it's odd to combine "way" with his secondary meaning "Weise, Methode". The verb "zeigen" would not be a very appropriate verb. Man kann eine Weise beschreiben, erklären, beleuchten, vorzeigen, illustrieren, erläutern, ... aber man zeigt den Weg, die Straße, das Gebäude, ganz einfach! There is no reason to become complicated, studying a language that is not simple at all. Cheers to all!
Where would word "bitte" go in this case? Does it make sense like this - Kannst du mir bitte den Weg zeigen?
bitte kind of acts like an adverb there, and those generally go as close after the verb as possible.
The subject (if it's not before the verb) comes even more closely behind the verb, followed by any personal pronouns there might be, and so Kannst du mir bitte... has the bitte as close behind the verb as possible, and that is the most natural position for it.