The ה is implied by the vocalization "lah-d'vorah". If it had been pronounced "l'd'vorah" where the vowel in the ל's syllable was very short (?), it would mean 'a bee' as opposed to "la-d'vorah" which means 'the bee'. Sorry, I can't type vowels and I don't really know how to talk about them in English, but I hope you get what I mean.
The same reason as giving them a name after animals like Raven, Lark, Robin, Kitty, Buck, Leo(n) in English. Or after plants, like Olive, Rosemary, Ginger, Jasmine, Daisy and many, many more. Some cultures have more of those, and some have less. I'd say both Hebrew and English are high on that spectrum.
I've never heard bees being associated with being stingy, just diligent.
This is a learning process. Sometimes we learn from being told what a word means; sometimes we learn from figuring out the meaning from the options presented to us. And sometimes we learn by making an error, seeing the correction, and getting it right the next time. It's all good.
I think your question was "Is it correct to choose a word provided in the options of a word which I do not remember/know ? " ?
I think not (if this is what you meant) because all the options under the word are correct synonyms, but not all can correctly fit into the context of the sentence.
Between our sentence "Does the bee have a tail?" and your sentence "Does a bee have a tail?" the only difference is the first vowel, which we hear in the audio as "LaDvorah" (instead of "LiDvorah" or "LeDvorah"). Without audio, we would need context or nikkud to make the distinction.
Deborah in hebrew is as I've said דבורה, but it cannot be "translated" as you don't and can't translate names, they only have a different form, but they are not translated (f.ex. William=Wilhelm=Guillaume=Guillermo etc.) . But to be honest I don't know what nesanef answered with 'No.' I think (s)he was talking about the question 'Does the bee have a tail?' but not sure... :/