Still hasn’t done something
Structure
- まだ + Verb[て] + いません
Two questions…
This is simply the progressive tense in the polite negative, yah?
Does it have to be in the polite? Would まだたべていない。 not work?
(I’m just a little confused as to why the other further reading (E-Japanese link) of this also has it specifically in the polite tense as well)
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It doesn’t have to be in the polite form. So yeah, まだたべていない works. See the video by Misa/Japanese Ammo
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It just show the polite form because in the N5 levels that’s often all people have been taught to use so far.
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During reviews it is difficult to know if BunPro is looking for the まだ～ていません or まだ grammar point. I am often getting it wrong by answering まだ～ていない. I think a warning message of [more polite] would work well here.
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I don’t know why this hasn’t occurred to me.
By why is it
「まだ～ていません」and not「まだ～ていませんでした」or「まだ～ませんでした」？
Hey @kariforuniajin !
Since でした means ‘was/were’ it will change the translation from ‘Still haven’t done (something)’ to ‘Still had not done (something)’.
Examples:
太郎くんはまだ来ていません。
Taro still hasn’t arrived.
太郎君はまだ来ていませんでした。
Taro had not arrived yet. (I checked earlier, but at the time I checked, he wasn’t here yet)
I hope this answers your question! 
ふがさん ありがとうございます！
Some of the alt answers to その本を still havent read include:
まだ読んでません
まだ読んでないです
Why are these correct? The other two
まだ読んでいません
まだ読んでいないです
Make sense since it has the conjugation of いる
There is no explanation about this in the text. Im so confused 
please help
For that, you have to reference a small footnote in ている② (JLPT N5) | Bunpro, い in ～ている can be omitted (and ～ていない is just a negative ～ている).