I did understand that the sentence means " the bee has honey", but it was marked wrong when I just tried the word-for-word translation : " for the bee, there is honey " , which also might be considered correct .
It would be To the bee there is honey but I don't think they're accepting literal translataions, probably mainly because you just wouldn't say that in English.
I would say you couldn't translate this sentence as Deborah has honey (I had been considering that) because the first word is pronounced "la dvorah." So that has to translate as "the bee" here.
Yes, but if it's a name, you don't add 'ה for definiteness, so instead of pronouncing "la'dvora", you'd say "le'dvora" (or, more correctly, "li'dvora").
Deborah is definite. However, the -ה prefix should not be used with names, just like you don't say "The Deborah has honey".
"Deborah has honey" could be accepted, I guess. Though the name is usually said with different emphasis nowadays (dvóra instead of dvorá for bee).
It seems to me that when a noun becomes a person's name, the acccent shifts to the first syllable. Is that correct?
Not the first, the one before last. But yes, it's common to change the stress to differentiate between the noun and the name.