Translation:Please do not look at magazines at school.
I'm not sure, but using 見る intead of 読む means the the sentence actually says "please do not look at magazines at school"
It should be. I reported it. I think they may be trying to impose the distinction between the Japanese locational particles DE (place of action) and NI (place of existence, etc.) inappropriately on English AT vs. IN.
"Please do not read magazines in school." was accepted, so other variations should probably be reported if they aren't already accepted.
With the word 'the,' you are referring to a delimited set of magazines, presumed by the speaker to be understood by the listener, whereas Duo's statement is general. Because Japanese lacks articles, as well as generally lacking specificity with regard to singular / plural, we might think what's the difference for Japanese speakers. The set might be indicated by a determiner or something a little more spelled out, if not clear from context: その雑誌、こういう雑誌、あそこの雑誌、つくえにある雑誌 ....
Why doesn't Duolingo allow the kanji for certain words in audio questions
It's still in beta, and I think they want to focus on speaking and hearing rather than writing
I think the point they're trying to make here is that 学校で refers to a location, at school, rather than a time frame, during school.
It's て directly after the stem of a vowel stem (=ichidan) verb, but after adding -ない- to any verb it's always で. There is another negative て form, -なくて, but you can't use in a command. That one takes て instead of で because the -k- in the syllable before it is an unvoiced consonant. There are a couple of tables in the Wikipedia article on Japanese verb conjugation that may be helpful, one of which is a PDF review sheet that you could download for quick reference: https://en.m.wikipedia.org/wiki/Japanese_verb_conjugation
Depending on the context, 見る can be translated not only as 'see,' but also as 'look at' or 'watch.' It's important when learning another language to realize that words in any language may have multiple meanings or uses and that you should not always expect a simple one to one correspondence of one word in a language to just one in another.