Translation:This experience will remain in my memory forever.
"This experience will remain forever in my memory" was counted wrong. This is ridiculous--the meaning is identical to the suggested answer, and to a native speaker it sounds normal either way in English.
It is very frustrating that Duolingo thinks it is always incorrect English sentence order to put time before other modifiers--this is not a strict rule in English and often the sentence sounds equally natural to a native speaker either way. And in any case, we are learning Spanish here--I am perfectly happy with my ability to speak English!
They both mean 'forever' but from what I've looked into, there does seem to be a slight distinction between the two. Por siempre refers to things that have already happened in the past and continued forward, while para siempre is for things that will continue forward from the present. Here's a good explanation I found: http://forum.wordreference.com/showthread.php?t=35098&p=5998359#post5998359
The rule for compound tenses of verbs is that the adverb usually goes after the first auxiliary. There's a good explanation here: http://www.englishtenses.com/adverbs_of_frequency_position Putting it before the auxiliary changes the meaning to put the emphasis on "will", so potentially it is not an accurate translation of the Spanish.
I disagree. It seems ambiguous because we often use "forever" as a prepositional adverb. i.e. "I'm leaving forever." However, in this case it is not a prepositional adverb, so it must come before the verb or after the preposition. Ask yourself if "This experience will be forever" makes sense without the preposition "in my memory." If it doesn't make sense without the preposition, then the adverb alone is not prepositional and should not follow the verb.
I don't see any ambiguity, k3nd0 -- all three seem clear and equivalent. And in "I'm leaving forever," the last word is an adverb but I don't think it is a prepositional one, since it can never function as a preposition. All the examples of prepostional adverbs I found were in phrases like "fall down, tune in, turn on, drop out," where the verb is completed by an adverb that commonly functions as a preposition.
You seem to be saying that an adverb that is not prepositional should not (immediately, I guess you meant) follow the verb, but in that case no one could ever fight bravely to his death.
Anyway, if the instance of "forever" in question is indeed a garden-variety adverb, it can go wherever it sounds natural. Even if there is a rule against it, which I doubt, I will continue to say "I am forever in your debt," grammarians be damned.