Translation:I do not write a lot of letters.
Well, you can make everything kani that has kanji, in theory, actually. There are some words that literally have no meaningful kanji (but could be spelt out with them, all the same) and there are words were the kanji are now truly obsolete, to all intents and purposes. However, many words are often spelt out in kana but have kanji for them which are still used, but many native Japanese don't really know.
Just as with any other people, Japanese are not all literate, knowledgeable people, many just about know the essentially mandatory 2000 or so kanji, others have pretty much all the taught kanji down and know others that are no longer required to be taught.
Hi! I'm sorry I've taken this long to answer that question. I'm not 100% sure why I wrote が instead of は there, but I can tell you the difference.
You use が when you're filling in a hole (answering a question). For example:
Would be answered with:
Where the が is highlighting that >>Yamada<< was the person who went.
If you'd said 山田さんは行きました。you're just stating that Yamada went, without any real emphasis.
あまり refers to the full sentence and not to the noun, so in a way, it's neither of them, since "hardly ever" is more about frequency and "not a lot" refers to the noun. Both should be accepted as a translation though, in my opinion. Of course, it's always contextual since you almost never can translate a word the same way all the time from one language to another.
Is "I don't write a lot of letters" the same as "I don't write letters a lot"? I think the former is talking about the quantity of letters and the latter is talking about frequency of doing something. あまり is adverb, right? So the latter should be the only one correct? (I still haven't tried "I don't often write letters")
Sorry for the dumb question but why is "I do not write letters" an incorrect answer? I thought あまり was like, "never" in this context.
There are no dumb questions! How else are you going to learn? :)
I'm trying to think of a context where I would use 「あまり」to mean "never." I suppose if someone were understating things... Nah, I can't think of any time I would use it to mean "never." Think of it as "not much" or "not often." If I wanted to say "never" in this sentence, I would use 「ぜんぜん」、or maybe to get a future context of "I would never," I might use 「ぜったいに」, and maybe even add an emphatic negative は to get 「ぜったいには」
Hope this helps!